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Algebra 1 : Distributive Property

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Example Questions

Example Question #351 : Algebra

Expand and combine like terms.

(x+2)(x-2)

Possible Answers:

x^2 + 4x - 4

$x^{2}+4$

$x^{2} +2x +4$

$x^{2} - 4$

Correct answer:

$x^{2} - 4$

Explanation:

Using the FOIL distribution method:

(x+2)(x-2)

First: x*x = x^2

Outer: x*-2= -2x

Inner: 2*x = 2x

Last: 2*-2 = -4

Resulting in: x^2 - 2x + 2x -4

Combining like terms, the 's cancel for a final answer of:

$x^{2} - 4$

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Example Question #31 : Distributive Property

Expand and combine like terms.

(x+2)(x+3)

Possible Answers:

$x^{2} +2x +3$

$x^{2} +5x +6$

$x^{2} +3x +2$

$x^{2} +5x -6$

$x^{2} +6x +5$

Correct answer:

$x^{2} +5x +6$

Explanation:

Using the FOIL distribution method:

(x+2)(x+3)

First: x*x = x^2

Outer: x*3= 3x

Inner: 2*x = 2x

Last: 2*3=6

Resulting in: x^2 +3x+2x+6

Combining like terms, the 's combine for a final answer of:

$x^{2} +5x +6$

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Example Question #4844 : Algebra 1

Expand and combine like terms.

(x-4)(x-7)

Possible Answers:

$x^{2} -4x -7$

$x^{2} -11x +28$

$x^{2} -11x -28$

$x^{2} -7x -4$

$x^{2} +11x -28$

Correct answer:

$x^{2} -11x +28$

Explanation:

Using the FOIL distribution method:

(x-4)(x-7)

First: x*x = x^2

Outer: x*-7= -7x

Inner: -4*x = -4x

Last: -4*-7=28

Resulting in: x^2 -4x-7x+28

Combining like terms, the 's combine for a final answer of:

$x^{2} -11x +28$

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Example Question #4845 : Algebra 1

Expand and combine like terms.

(x+5)(x-8)

Possible Answers:

$x^{2} +3x-40$

$x^{2} +13x-40$

$x^{2} -8x+5$

$x^{2} -3x-40$

$x^{2} -3x+13$

Correct answer:

$x^{2} -3x-40$

Explanation:

Using the FOIL distribution method:

(x+5)(x-8)

First: x*x = x^2

Outer: x*-8= -8x

Inner: 5*x = 5x

Last: 5*-8=-40

Resulting in: x^2 -8x+5x-40

Combining like terms, the 's combine for a final answer of:

$x^{2} -3x-40$

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Example Question #4846 : Algebra 1

Expand and combine like terms.

(x-2)(x+10)

Possible Answers:

$x^{2} +2x +12$

$x^{2} +10x -2$

$x^{2} +12x -20$

$x^{2} +5x +12$

$x^{2} +8x -20$

Correct answer:

$x^{2} +8x -20$

Explanation:

Using the FOIL distribution method:

(x-2)(x+10)

First: x*x = x^2

Outer: x*10= 10x

Inner: -2*x = -2x

Last: -2*10=-20

Resulting in: x^2 +10x-2x-20

Combining like terms, the 's combine for a final answer of:

$x^{2} +8x -20$

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Example Question #4847 : Algebra 1

We usually use the FOIL method of distribution for expanding polynomials, but it is actually a property of numbers. Try to solve the product by foiling instead of computing directly.

52*52=(50+2)(50+2)

Possible Answers:

2504

249 8

2496

2704

104

Correct answer:

2704

Explanation:

Using the FOIL distribution method:

(50+2)(50+2)

First: 50*50 = 2500

Outer: 50*2= 100

Inner: 2*50 = 100

Last: 2*2=4

Resulting in: 2500 + 100 +100 +4 = 2704

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Example Question #31 : Distributive Property

We usually use the FOIL method of distribution for expanding polynomials, but it is actually a property of numbers. Try to solve the product by foiling instead of computing directly.

33*44=(30+3)(40+4)

Possible Answers:

252

1452

1512

1200

1212

Correct answer:

1452

Explanation:

Using the FOIL distribution method:

(30+3)(40+4)

First: 30*40 = 1200

Outer: 30*4= 120

Inner: 3*40 = 120

Last: 3*4=12

Resulting in: 1200 + 120 +120 +12 = 1452

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Example Question #32 : Distributive Property

Expand and simplify.

(5x + t)(2x + 3t)

Possible Answers:

x^2 + 5xt + 3t^2

10x^2 + 13xt + 3t^2

10x^2 + 17xt + 3t^2

10x^2 + 17x + 3t

x^2 + 7x + 4

Correct answer:

10x^2 + 17xt + 3t^2

Explanation:

Using the FOIL distribution method:

(5x + t)(2x + 3t)

First: 5x*2x = 10x^2

Outer: 5x*3t= 15x t

Inner: t*2x = 2xt

Last: t*3t=3t^2

Resulting in: 10x^2 + 15xt + 2xt + 3t^2

Combining like terms, the 's combine for a final answer of:

10x^2 + 17xt + 3t^2

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Example Question #33 : Distributive Property

Expand and simplify.

(x + y)(x - y)

Possible Answers:

x^2 + y^2

x^2 -2xy + y^2

x^2 +xy- y^2

x^2 - y^2

x^2 +2xy + y^2

Correct answer:

x^2 - y^2

Explanation:

Using the FOIL distribution method:

(x + y)(x - y)

First: x*x = x^2

Outer: x*-y= -xy

Inner: y*x = xy

Last: y*-y=-y^2

Resulting in: x^2 - xy + xy - y^2

Combining like terms, the 's cancel for a final answer of:

x^2 - y^2

Expressions of this form are commonly referred to as "difference of squares". If you can spot them, they are easy to expand and to factor because the middle terms always cancel.

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Example Question #34 : Distributive Property

Expand by FOILing:

(x+7)(x-2)

Possible Answers:

x^2-9x-14

x^2+5x-14

x^2-5x-14

x^2+9x-14

Correct answer:

x^2+5x-14

Explanation:

First: (x)(x)=x^2

Outside: (x)(-2)=-2x

Inside: (x)(7)=7x

Last: (-2)(7)=-14

Add the values together and combine like terms:

x^2-2x+7x-14=x^2+5x-14

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Algebra 1 : Distributive Property

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #351 : Algebra

Example Question #31 : Distributive Property

Example Question #4844 : Algebra 1

Example Question #4845 : Algebra 1

Example Question #4846 : Algebra 1

Example Question #4847 : Algebra 1

Example Question #31 : Distributive Property

Example Question #32 : Distributive Property

Example Question #33 : Distributive Property

Example Question #34 : Distributive Property

All Algebra 1 Resources

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