Simplifying Expressions Worksheets - Math Monks - Free Printable

Let’s solve each problem step by step. We’ll simplify each algebraic expression by combining like terms and using the distributive property where needed.

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1) 5(a + 6) - 2(7a + 5)

First, distribute:
- 5 × a = 5a
- 5 × 6 = 30
- -2 × 7a = -14a
- -2 × 5 = -10

Now write it all out:
5a + 30 - 14a - 10

Combine like terms:
- (5a - 14a) = -9a
- (30 - 10) = 20

→ -9a + 20

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2) 10y + 36 - 38y - 47

Group y terms and constants:
- (10y - 38y) = -28y
- (36 - 47) = -11

→ -28y - 11

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3) -8(-5x + 7) + 5x

Distribute -8:
- -8 × -5x = 40x
- -8 × 7 = -56

So: 40x - 56 + 5x

Combine x terms: 40x + 5x = 45x

→ 45x - 56

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4) -8(x - 6) + 20(x + 10)

Distribute both:
- -8 × x = -8x
- -8 × -6 = +48
- 20 × x = 20x
- 20 × 10 = 200

Write it out: -8x + 48 + 20x + 200

Combine x terms: (-8x + 20x) = 12x
Constants: 48 + 200 = 248

→ 12x + 248

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5) -2x + (3/2)x

We need to combine these. Think of -2x as -4/2 x.

So: -4/2 x + 3/2 x = (-4 + 3)/2 x = -1/2 x

→ -½x or -\frac{1}{2}x

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6) -6x + 8(3 - 8x)

Distribute 8:
- 8 × 3 = 24
- 8 × -8x = -64x

So: -6x + 24 - 64x

Combine x terms: -6x - 64x = -70x

→ -70x + 24

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7) (5/7)(-8/5 k + 1)

Distribute 5/7 to both terms inside:

First term: (5/7) × (-8/5 k)
Multiply numerators: 5 × -8 = -40
Denominators: 7 × 5 = 35
So: -40/35 k → simplify: divide numerator and denominator by 5 → -8/7 k

Second term: (5/7) × 1 = 5/7

→ -⁸⁄k + ⁵₇

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8) -8(2y) + 9 - 15 + 13y

First, multiply: -8 × 2y = -16y

Now rewrite: -16y + 9 - 15 + 13y

Group y terms: -16y + 13y = -3y
Constants: 9 - 15 = -6

→ -3y - 6

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9) 4(3t + 8) + 8

Distribute 4:
- 4 × 3t = 12t
- 4 × 8 = 32

So: 12t + 32 + 8

Add constants: 32 + 8 = 40

→ 12t + 40

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10) 8x + 6 - 7x + 7 + 3x + 2

Group x terms: 8x - 7x + 3x = (8 - 7 + 3)x = 4x
Constants: 6 + 7 + 2 = 15

→ 4x + 15

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Final Answer:
1) -9a + 20
2) -28y - 11
3) 45x - 56
4) 12x + 248
5) -½x
6) -70x + 24
7) -⁸₇k + ⁵⁄₇
8) -3y - 6
9) 12t + 40
10) 4x + 15