The distributive property of addition and multiplication states that multiplying a sum by a number is the same as multiplying each addend by that number and then adding the two products. For example, 3(2 + 4) = (3 • 2) + (3 • 4)

The following video shows some examples of the distributive property.

Using the distributive property in algebra.

Solving Equations using Distributive Property

To solve algebra equations using the distributive property, we need to distribute (or multiply) the number with each term in the expression. In that way, the brackets are removed. We can then combine like terms and solve by equivalent equations when necessary.

Remember to apply the following rules for sign multiplication when necessary.

[3 • 2x] + [3 • 5] = 3 (use distributive property)
6x + 15 = 3 (subtract 15 from both sides)
6x = –12 (divide 6 on both sides) x = –2

Check:

3(2x + 5) = 3 (substitute x = –2 into the original equation)
3((2 • –2) + 5) = 3

Example:

Solve
2x – 2(3x – 2) = 2(x –2) + 20

Solution:

2x – 2(3x – 2) = 2(x –2) + 20
2x – 6x + 4 = 2x – 4 + 20 (use distributive property)
– 4x + 4 = 2x + 16 (combine like terms)
–4x + 4 – 4 –2x = 2x + 16 – 4 –2x(add or subtract on both sides)
–6x = 12 (divide both sides by –6) x = –2

Check:

2x – 2(3x – 2) = 2(x –2) + 20 (substitute x = –2 into the original equation)
(2 • –2) – 2((3 • –2) –2) = 2(–2 –2) + 20
12 = 12

Videos

The following video shows some examples of solving multi-step equation by distributive property and combine like terms.

Solving Equations with the Distributive Property

Solving equations with the distributive property 2

Solve multi-step equations using the distributive property

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