How to Use the Distributive Property to Remove Parentheses

Distributive property allows you to create equivalent expressions.

The distributive property is one of the basic algebraic properties. This property allows you to multiply one number throughout an expression or equation to simplify the expression or equation. The distributive property works by applying the same multiplication to each term in an expression or equation. Once the distributive property is applied, the parentheses can usually be dropped.



In algebraic terms, the distributive property looks like this: a(b+c) = a*b + a*c. This property can be used for multiplying two or more polynomials.

Instructions

Mononial (One Term) by Polynomial (Multiple Terms)

1. Multiply the outside term by the first term inside the parentheses. For example:

   7(8x+5) --> 56x

   2(3y-4) --> 6y

   (1/2) (4z+8) --> 2z

2. Multiply the outside term by the next term inside the parentheses. For example:

   7(8x+5) --> 56x + 35

   2(3y-4) --> 6y - 8

   (1/2) (4z+8) --> 2z + 4

   If there are more than two terms inside the parentheses, this step is repeated for each term.

3. Combine any like terms. For example:

   6(7y+2x-8y) --> 42y+12x-48y --> 12x-6y

Two Polynomials

1. Multiply the first term of the first polynomial by the first term of the second polynomial. For example:

   (4x+8y)(4+3y) --> 16x

   (x+y)(2x-4y+3) --> 2x^2

2. Multiply the first term of the first polynomial by the next term in the second polynomial. This stepis repeated for each term in the second polynomial. For example:

   (4x+8y)(4+3y) --> 16x + 12xy

   (x+y)(2x-4y+3) --> 2x^2 -4xy + 3x

3. Multiply the second term of the first polynomial times each term in the second polynomial. For example:

   (4x+8y)(4+3y) --> 16x + 12xy + 32y + 24y^2

   (x+y)(2x-4y+3) --> 2x^2 -4xy + 3x +2xy - 4y^2 + 3y

4. Combine like terms. For example:

   (4x+8y)(4+3y) --> 16x + 12xy + 32y + 24y^2 (No like terms to combine.)

   (x+y)(2x-4y+3) --> 2x^2 -4xy + 3x +2xy - 4y^2 + 3y --> 2x^2 = 3x -2xy +3y - 4y^2

Tips & Warnings

• Watch the signs that are with each term. The most common mistake is not using the correct sign with the term.

References

• Purple Math - Number Properties
• Algebra Help - Distribution Property