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What is distributive property? is a mathematical concept that involves the multiplication of a number by the sum or difference of two or more numbers. Learn more about what is distributive property by reading below.
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What is distributive property?
The distributive property is a fundamental property of arithmetic and algebra that explains how to distribute a factor outside of a set of parentheses to each term inside the parentheses. Specifically, the distributive property states that:
a(b + c) = ab + ac
This means that when we multiply a number a by the sum of two other numbers b and c, we can either distribute a to both b and c separately and then add the results, or we can add b and c together first and then multiply the sum by a.
For example, suppose we want to evaluate the expression 3(4 + 5). Using the distributive property, we can rewrite this expression as:
3(4 + 5) = 3(4) + 3(5)
= 12 + 15
= 27
Here, we distributed the factor 3 to both 4 and 5 separately and then added the resulting products to get the final answer of 27.
The distributive property is a key tool in simplifying algebraic expressions, especially those involving variables. For example, suppose we want to simplify the expression 2x(x + 3). Using the distributive property, we can rewrite this expression as:
2x(x + 3) = 2xx + 2×3
= 2x^2 + 6x
Here, we distributed the factor 2x to both x and 3 separately and then added the resulting products to get the final simplified expression of 2x^2 + 6x.
The distributive property also works in reverse, which is sometimes called factoring. For example, suppose we have the expression 6x + 12. Using the distributive property in reverse, we can factor out the common factor of 6 to get:
6x + 12 = 6(x + 2)
Here, we distributed the factor 6 to both x and 2 separately and then combined them to get the final factored expression of 6(x + 2).
In summary, the distributive property is a powerful tool that allows us to simplify expressions and perform calculations more efficiently. It is a fundamental concept in mathematics that is used extensively in algebra, calculus, and other fields.
What is distributive property and example?
In mathematics, the distributive property is a property of operations that states that when one operation is performed on the sum or difference of two numbers, the operation can be distributed or applied to each number within the parentheses. This property is often used in algebraic expressions and equations to simplify or solve problems.
The distributive property is commonly expressed as follows:
a(b + c) = ab + ac
or
a(b – c) = ab – ac
where a, b, and c are any real numbers.
For example, let’s say we have the expression 3(2 + 4). Using the distributive property, we can distribute the 3 to each term inside the parentheses, as follows:
3(2 + 4) = 3(2) + 3(4) = 6 + 12 = 18
Similarly, we can use the distributive property to simplify more complex expressions. For example, consider the expression
2(x + 3) – 4(x – 1)
Using the distributive property, we can distribute the coefficients 2 and -4 to each term inside the parentheses, as follows:
2(x + 3) – 4(x – 1) = 2x + 6 – 4x + 4
We can then simplify this expression by combining like terms, as follows:
2x + 6 – 4x + 4 = -2x + 10
Therefore,
2(x + 3) – 4(x – 1) = -2x + 10
The distributive property can also be used to solve equations. For example, consider the equation
4(x + 2) = 20
We can use the distributive property to simplify this equation, as follows:
4(x + 2) = 20
4x + 8 = 20
We can then solve for x by isolating the variable on one side of the equation, as follows:
4x + 8 = 20
4x = 20 – 8
4x = 12
x = 3
Therefore, the solution to the equation 4(x + 2) = 20 is x = 3.
In summary, the distributive property is an important property of operations in mathematics that allows us to simplify algebraic expressions and equations by distributing operations to each term inside parentheses. This property is used extensively in algebra, and its understanding is crucial for solving equations and simplifying complex expressions.
What is the rule for distributive property?
The distributive property is a fundamental rule in mathematics that allows us to simplify expressions and perform calculations more efficiently. The rule states that when we multiply a number by a sum of two or more numbers, we can distribute the multiplication across each term in the sum. In other words, we can multiply each term in the sum by the number and then add the resulting products.
The general rule for the distributive property is:
a(b + c) = ab + ac
where a, b, and c are any real numbers or algebraic expressions.
This means that if we have a number or expression outside a set of parentheses that contain a sum of two or more numbers or expressions, we can multiply the number or expression outside the parentheses by each term inside the parentheses and then add the resulting products.
For example, let’s say we have the expression:
2(x + 3)
To apply the distributive property, we can distribute the multiplication of 2 across the sum of x and 3 as follows:
2(x + 3) = 2x + 2(3)
Simplifying further:
2(x + 3) = 2x + 6
We can also use the distributive property in reverse to factorize expressions. For example, let’s say we have the expression:
4x + 8
To factorize this expression, we can use the distributive property in reverse as follows:
4x + 8 = 4(x + 2)
This means that we can factor out the common factor of 4 from the expression 4x + 8 by dividing each term by 4.
The distributive property can be applied to more complex expressions as well, such as polynomials. For example, let’s say we have the expression:
3x^2 + 4x – 5(x + 2)
To simplify this expression, we can distribute the multiplication of -5 across the sum inside the parentheses as follows:
3x^2 + 4x – 5(x + 2) = 3x^2 + 4x – 5x – 10
Simplifying further:
3x^2 – x – 10
By applying the distributive property, we have simplified the original expression and reduced it to a simpler form.
In summary, the distributive property is a rule in mathematics that allows us to simplify expressions by distributing the multiplication of a number or expression across a sum of two or more numbers or expressions. The rule can be applied in various contexts, from simple arithmetic to algebraic expressions and polynomials. By applying the distributive property, we can make calculations and simplifications more efficient and precise.
Distributive property formula
The distributive property is a mathematical property that states that when multiplying a number by a sum or difference of two or more terms, the result is the same as multiplying each term individually by the number and then adding or subtracting the products. This can be written as:
a(b + c) = ab + ac
a(b – c) = ab – ac
where “a” is the number being multiplied, and “b” and “c” are the terms being added or subtracted.
The distributive property can also be applied in reverse, where a common factor can be factored out of a sum or difference of terms. For example:
3x + 6y = 3(x + 2y)
In this case, the common factor of 3 is factored out of the sum of 3x and 6y.
The distributive property can be used to simplify algebraic expressions by reducing the number of terms and operations involved. For example:
2(x + 3) + 4(x + 1)
= 2x + 6 + 4x + 4 (distributing the 2 and 4)
= 6x + 10 (combining like terms)
The distributive property can also be used in conjunction with other algebraic properties, such as the associative and commutative properties, to simplify more complex expressions. For example:
2(3x + 4) – 3(2x – 1)
= 6x + 8 – 6x + 3 (distributing the 2 and -3)
= 11 (combining like terms)
The distributive property is a fundamental property in algebra and is used extensively in various mathematical applications, such as solving equations, simplifying expressions, and factorizing polynomials. Understanding and applying the distributive property is essential in developing algebraic skills and solving problems in mathematics.
What is the distributive property steps?
The distributive property is a fundamental rule in mathematics that allows us to simplify expressions by breaking them down into smaller parts. The basic idea behind the distributive property is that we can distribute a factor to each term inside a set of parentheses. The steps for using the distributive property are as follows:
Step 1: Identify any terms that can be combined inside the parentheses. For example, if we have the expression 3(x + 4), we can see that x and 4 are both terms inside the parentheses.
Step 2: Multiply the factor outside the parentheses by each term inside the parentheses. In the example above, we would multiply 3 by x and 3 by 4 to get 3x + 12.
Step 3: Replace the original expression with the simplified expression. In our example, we can replace 3(x + 4) with 3x + 12.
Let’s look at another example to see the distributive property in action:
Example: Simplify the expression 2(3x + 5)
Step 1: Identify the terms inside the parentheses, which are 3x and 5.
Step 2: Multiply the factor outside the parentheses, which is 2, by each term inside the parentheses. This gives us:
2(3x) + 2(5) = 6x + 10
Step 3: Replace the original expression with the simplified expression, which is 6x + 10.
The distributive property can also be used in reverse to factor out a common factor from an expression. To use the distributive property in reverse, we follow these steps:
Step 1: Identify a common factor in all the terms of the expression. For example, in the expression 6x + 12, both terms have a common factor of 6.
Step 2: Factor out the common factor from each term. In our example, we would factor out 6 to get:
6(x + 2)
Step 3: Replace the original expression with the factored expression.
The distributive property is a powerful tool that allows us to simplify expressions and solve equations more easily. It is an essential concept in algebra and is used in a wide range of mathematical applications.
What is distributive property – FAQ
1. What is distributive property in math?
Distributive property is a property in math that allows us to distribute a factor to each term inside a set of parentheses or brackets.
2. How is the distributive property useful in math?
The distributive property is useful in simplifying algebraic expressions and solving equations.
3. What is the formula for the distributive property?
The formula for the distributive property is a(b+c) = ab + ac or (a+b)c = ac + bc.
4. Can the distributive property be applied to addition?
No, the distributive property only applies to multiplication and division.
5. Can the distributive property be applied to division?
Yes, the distributive property can be applied to division. For example, a/(b+c) can be distributed as a/b + a/c.
6. What is an example of the distributive property?
An example of the distributive property is 3(2x + 5) = 6x + 15.
7. Can the distributive property be used with negative numbers?
Yes, the distributive property can be used with negative numbers. For example, -2(x+3) can be distributed as -2x – 6.
8. How can the distributive property be used to solve equations?
The distributive property can be used to simplify equations by distributing a factor to each term, which can then be combined and solved.
9. Can the distributive property be used with fractions?
Yes, the distributive property can be used with fractions. For example, (1/2)(4x+6) can be distributed as 2x+3.
10. What is the inverse of the distributive property?
The inverse of the distributive property is combining like terms.
11. What is the associative property of multiplication?
The associative property of multiplication allows us to change the grouping of factors in a multiplication expression without changing the result. For example, (ab)c = a(bc).
12. What is the commutative property of multiplication?
The commutative property of multiplication allows us to change the order of factors in a multiplication expression without changing the result. For example, ab = ba.
13. What is the identity property of multiplication?
The identity property of multiplication states that any number multiplied by 1 is equal to itself. For example, a x 1 = a.
14. Can the distributive property be used with polynomials?
Yes, the distributive property can be used with polynomials. For example, (3x+4)(2x-5) can be distributed as 6x^2-7x-20.
15. What is the purpose of using the distributive property in algebraic expressions?
The purpose of using the distributive property in algebraic expressions is to simplify them by combining like terms.
16. Can the distributive property be used in geometry?
Yes, the distributive property can be used in geometry to find the perimeter or area of complex shapes.
17. What is the distributive property of exponents?
The distributive property of exponents allows us to simplify expressions with exponents by multiplying the bases and adding the exponents. For example, a^m x a^n = a^(m+n).
18. What is the distributive property of fractions?
The distributive property of fractions allows us to simplify expressions with fractions by distributing a factor to each term. For example, a(b/c) = ab/c.
19. Can the distributive property be used to solve inequalities?
Yes, the distributive property can be used to solve inequalities by distributing a factor and solving for the variable.
20. How can the distributive property be used to factor polynomials?
The distributive property is a useful tool for factoring polynomials.
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