Multiplying Binomials worksheets - Free Printable

Let’s solve each problem step by step. We’re multiplying two binomials — that means we use the distributive property (also called FOIL: First, Outer, Inner, Last).

We’ll go one by one and show the work for each.

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1) (-10x - 3)(-5x + 1)

First: (-10x)(-5x) = 50x²
Outer: (-10x)(1) = -10x
Inner: (-3)(-5x) = 15x
Last: (-3)(1) = -3

Combine like terms: -10x + 15x = 5x
→ 50x² + 5x - 3

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2) (-9x - 2)(-4x + 5)

First: (-9x)(-4x) = 36x²
Outer: (-9x)(5) = -45x
Inner: (-2)(-4x) = 8x
Last: (-2)(5) = -10

Combine: -45x + 8x = -37x
→ 36x² - 37x - 10

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3) (-1x - 7)(5x + 4)

First: (-1x)(5x) = -5x²
Outer: (-1x)(4) = -4x
Inner: (-7)(5x) = -35x
Last: (-7)(4) = -28

Combine: -4x -35x = -39x
→ -5x² - 39x - 28

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4) (-5x - 8)(2x + 1)

First: (-5x)(2x) = -10x²
Outer: (-5x)(1) = -5x
Inner: (-8)(2x) = -16x
Last: (-8)(1) = -8

Combine: -5x -16x = -21x
→ -10x² - 21x - 8

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5) (-7x - 9)(3x + 1)

First: (-7x)(3x) = -21x²
Outer: (-7x)(1) = -7x
Inner: (-9)(3x) = -27x
Last: (-9)(1) = -9

Combine: -7x -27x = -34x
→ -21x² - 34x - 9

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6) (-2x - 6)(-5x + 2)

First: (-2x)(-5x) = 10x²
Outer: (-2x)(2) = -4x
Inner: (-6)(-5x) = 30x
Last: (-6)(2) = -12

Combine: -4x + 30x = 26x
→ 10x² + 26x - 12

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7) (-9x - 4)(-1x + 4)

First: (-9x)(-1x) = 9x²
Outer: (-9x)(4) = -36x
Inner: (-4)(-1x) = 4x
Last: (-4)(4) = -16

Combine: -36x + 4x = -32x
→ 9x² - 32x - 16

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8) (-5x - 7)(1x + 2)

First: (-5x)(1x) = -5x²
Outer: (-5x)(2) = -10x
Inner: (-7)(1x) = -7x
Last: (-7)(2) = -14

Combine: -10x -7x = -17x
→ -5x² - 17x - 14

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9) (-6x - 9)(2x + 5)

First: (-6x)(2x) = -12x²
Outer: (-6x)(5) = -30x
Inner: (-9)(2x) = -18x
Last: (-9)(5) = -45

Combine: -30x -18x = -48x
→ -12x² - 48x - 45

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10) (-8x - 2)(3x + 3)

First: (-8x)(3x) = -24x²
Outer: (-8x)(3) = -24x
Inner: (-2)(3x) = -6x
Last: (-2)(3) = -6

Combine: -24x -6x = -30x
→ -24x² - 30x - 6

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11) (-6x - 1)(3x + 1)

First: (-6x)(3x) = -18x²
Outer: (-6x)(1) = -6x
Inner: (-1)(3x) = -3x
Last: (-1)(1) = -1

Combine: -6x -3x = -9x
→ -18x² - 9x - 1

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12) (-6x - 10)(3x + 2)

First: (-6x)(3x) = -18x²
Outer: (-6x)(2) = -12x
Inner: (-10)(3x) = -30x
Last: (-10)(2) = -20

Combine: -12x -30x = -42x
→ -18x² - 42x - 20

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13) (-3x - 8)(2x + 4)

First: (-3x)(2x) = -6x²
Outer: (-3x)(4) = -12x
Inner: (-8)(2x) = -16x
Last: (-8)(4) = -32

Combine: -12x -16x = -28x
→ -6x² - 28x - 32

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14) (-5x - 4)(1x + 1)

First: (-5x)(1x) = -5x²
Outer: (-5x)(1) = -5x
Inner: (-4)(1x) = -4x
Last: (-4)(1) = -4

Combine: -5x -4x = -9x
→ -5x² - 9x - 4

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15) (-7x - 2)(3x + 5)

First: (-7x)(3x) = -21x²
Outer: (-7x)(5) = -35x
Inner: (-2)(3x) = -6x
Last: (-2)(5) = -10

Combine: -35x -6x = -41x
→ -21x² - 41x - 10

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16) (-4x - 10)(1x + 1)

First: (-4x)(1x) = -4x²
Outer: (-4x)(1) = -4x
Inner: (-10)(1x) = -10x
Last: (-10)(1) = -10

Combine: -4x -10x = -14x
→ -4x² - 14x - 10

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17) (-3x - 7)(-4x + 5)

First: (-3x)(-4x) = 12x²
Outer: (-3x)(5) = -15x
Inner: (-7)(-4x) = 28x
Last: (-7)(5) = -35

Combine: -15x + 28x = 13x
→ 12x² + 13x - 35

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18) (-6x - 8)(-1x + 2)

First: (-6x)(-1x) = 6x²
Outer: (-6x)(2) = -12x
Inner: (-8)(-1x) = 8x
Last: (-8)(2) = -16

Combine: -12x + 8x = -4x
→ 6x² - 4x - 16

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19) (-7x - 4)(3x + 4)

First: (-7x)(3x) = -21x²
Outer: (-7x)(4) = -28x
Inner: (-4)(3x) = -12x
Last: (-4)(4) = -16

Combine: -28x -12x = -40x
→ -21x² - 40x - 16

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20) (-6x - 3)(4x + 3)

First: (-6x)(4x) = -24x²
Outer: (-6x)(3) = -18x
Inner: (-3)(4x) = -12x
Last: (-3)(3) = -9

Combine: -18x -12x = -30x
→ -24x² - 30x - 9

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21) (-4x - 5)(3x + 3)

First: (-4x)(3x) = -12x²
Outer: (-4x)(3) = -12x
Inner: (-5)(3x) = -15x
Last: (-5)(3) = -15

Combine: -12x -15x = -27x
→ -12x² - 27x - 15

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22) (-1x - 3)(-5x + 3)

First: (-1x)(-5x) = 5x²
Outer: (-1x)(3) = -3x
Inner: (-3)(-5x) = 15x
Last: (-3)(3) = -9

Combine: -3x + 15x = 12x
→ 5x² + 12x - 9

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23) (-8x - 7)(3x + 4)

First: (-8x)(3x) = -24x²
Outer: (-8x)(4) = -32x
Inner: (-7)(3x) = -21x
Last: (-7)(4) = -28

Combine: -32x -21x = -53x
→ -24x² - 53x - 28

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24) (-4x - 8)(3x + 2)

First: (-4x)(3x) = -12x²
Outer: (-4x)(2) = -8x
Inner: (-8)(3x) = -24x
Last: (-8)(2) = -16

Combine: -8x -24x = -32x
→ -12x² - 32x - 16

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25) (-2x - 3)(-3x + 2)

First: (-2x)(-3x) = 6x²
Outer: (-2x)(2) = -4x
Inner: (-3)(-3x) = 9x
Last: (-3)(2) = -6

Combine: -4x + 9x = 5x
→ 6x² + 5x - 6

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26) (-10x - 1)(-5x + 1)

First: (-10x)(-5x) = 50x²
Outer: (-10x)(1) = -10x
Inner: (-1)(-5x) = 5x
Last: (-1)(1) = -1

Combine: -10x + 5x = -5x
→ 50x² - 5x - 1

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27) (-2x - 8)(2x + 5)

First: (-2x)(2x) = -4x²
Outer: (-2x)(5) = -10x
Inner: (-8)(2x) = -16x
Last: (-8)(5) = -40

Combine: -10x -16x = -26x
→ -4x² - 26x - 40

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28) (-10x - 2)(2x + 5)

First: (-10x)(2x) = -20x²
Outer: (-10x)(5) = -50x
Inner: (-2)(2x) = -4x
Last: (-2)(5) = -10

Combine: -50x -4x = -54x
→ -20x² - 54x - 10

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29) (-3x - 9)(3x + 1)

First: (-3x)(3x) = -9x²
Outer: (-3x)(1) = -3x
Inner: (-9)(3x) = -27x
Last: (-9)(1) = -9

Combine: -3x -27x = -30x
→ -9x² - 30x - 9

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30) (-8x - 1)(3x + 2)

First: (-8x)(3x) = -24x²
Outer: (-8x)(2) = -16x
Inner: (-1)(3x) = -3x
Last: (-1)(2) = -2

Combine: -16x -3x = -19x
→ -24x² - 19x - 2

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Final Answer:
1) 50x² + 5x - 3
2) 36x² - 37x - 10
3) -5x² - 39x - 28
4) -10x² - 21x - 8
5) -21x² - 34x - 9
6) 10x² + 26x - 12
7) 9x² - 32x - 16
8) -5x² - 17x - 14
9) -12x² - 48x - 45
10) -24x² - 30x - 6
11) -18x² - 9x - 1
12) -18x² - 42x - 20
13) -6x² - 28x - 32
14) -5x² - 9x - 4
15) -21x² - 41x - 10
16) -4x² - 14x - 10
17) 12x² + 13x - 35
18) 6x² - 4x - 16
19) -21x² - 40x - 16
20) -24x² - 30x - 9
21) -12x² - 27x - 15
22) 5x² + 12x - 9
23) -24x² - 53x - 28
24) -12x² - 32x - 16
25) 6x² + 5x - 6
26) 50x² - 5x - 1
27) -4x² - 26x - 40
28) -20x² - 54x - 10
29) -9x² - 30x - 9
30) -24x² - 19x - 2