M
Math Coach Amy
Amy Ferguson Moncure

Simplifying Expressions

Distribute • Watch the signs • Combine like terms

Jump to section:

What to Remember

Distribute to every term

Multiply the outside number by every term inside the parentheses, including the negative ones.

$$3(x-4)+5x=3x-12+5x$$

Combine like terms.

$$8x-12$$

A minus distributes too

A negative outside, or a minus in front of parentheses, changes the sign of every term inside.

$$2(x-1)-3(x+4)=2x-2-3x-12$$

Combine like terms.

$$-x-14$$

Nested parentheses

Work inside first. Distribute the inner grouping, then the outer one.

$$5-3[x-7(2x-6)]=5-3[x-14x+42]$$

$$5-3x+42x-126$$

Combine like terms.

$$39x-121$$

Level 1

Easy

One set of parentheses. Distribute, then combine like terms.

1

Simplify. \( 5(x-3)+2x \)

Show Answer

\(5x-15+2x\)

Combine like terms.

Answer: \(7x-15\)

2

Simplify. \( -3(x-4)+2 \)

Show Answer

\(-3x+12+2\)

Combine like terms.

Answer: \(-3x+14\)

Level 2

Medium

Work inside the grouping first. Distribute both positive and negative terms, then combine like terms.

3

Simplify. \( 4-2[x-6(2x-3)] \)

Show Answer

\(4-2[x-12x+18]\)

\(4-2x+24x-36\)

Combine like terms.

Answer: \(22x-32\)

4

Simplify. \( 3(x+4)-2(3x-5) \)

Show Answer

\(3x+12-6x+10\)

Combine like terms.

Answer: \(-3x+22\)

5

Simplify. \( 6+4[x-3(2x-5)] \)

Show Answer

\(6+4[x-6x+15]\)

\(6+4x-24x+60\)

Combine like terms.

Answer: \(-20x+66\)

6

Simplify. \( 8-5[x+2(3x-4)] \)

Show Answer

\(8-5[x+6x-8]\)

\(8-5x-30x+40\)

Combine like terms.

Answer: \(-35x+48\)

Need help making distribute-and-combine automatic?

Book a Session with Amy