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Algebra 1 : Distributive Property

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Example Questions

Example Question #31 : Distributive Property

Expand and combine like terms.

$\displaystyle (x+2)(x-2)$

Possible Answers:

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

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

$x^{2} - 4$ $\displaystyle x^{2} - 4$

$\displaystyle x^2 +4x -2$

$\displaystyle x^2 + 4x - 4$

Correct answer:

$x^{2} - 4$ $\displaystyle x^{2} - 4$

Explanation:

Using the FOIL distribution method:

$\displaystyle (x+2)(x-2)$

First: $\displaystyle x*x = x^2$

Outer: $\displaystyle x*-2= -2x$

Inner: $\displaystyle 2*x = 2x$

Last: $\displaystyle 2*-2 = -4$

Resulting in: $\displaystyle x^2 - 2x + 2x -4$

Combining like terms, the $\displaystyle x$'s cancel for a final answer of:

$x^{2} - 4$ $\displaystyle x^{2} - 4$

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Example Question #32 : Distributive Property

Expand and combine like terms.

$\displaystyle (x+2)(x+3)$

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Using the FOIL distribution method:

$\displaystyle (x+2)(x+3)$

First: $\displaystyle x*x = x^2$

Outer: x*3= 3x $\displaystyle x*3= 3x$

Inner: $\displaystyle 2*x = 2x$

Last: 2*3=6 $\displaystyle 2*3=6$

Resulting in: $\displaystyle x^2 +3x+2x+6$

Combining like terms, the $\displaystyle x$'s combine for a final answer of:

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

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Example Question #4844 : Algebra 1

Expand and combine like terms.

$\displaystyle (x-4)(x-7)$

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Using the FOIL distribution method:

$\displaystyle (x-4)(x-7)$

First: $\displaystyle x*x = x^2$

Outer: $\displaystyle x*-7= -7x$

Inner: $\displaystyle -4*x = -4x$

Last: $\displaystyle -4*-7=28$

Resulting in: $\displaystyle x^2 -4x-7x+28$

Combining like terms, the $\displaystyle x$'s combine for a final answer of:

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

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Example Question #31 : Distributive Property

Expand and combine like terms.

$\displaystyle (x+5)(x-8)$

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Using the FOIL distribution method:

$\displaystyle (x+5)(x-8)$

First: $\displaystyle x*x = x^2$

Outer: $\displaystyle x*-8= -8x$

Inner: $\displaystyle 5*x = 5x$

Last: $\displaystyle 5*-8=-40$

Resulting in: $\displaystyle x^2 -8x+5x-40$

Combining like terms, the $\displaystyle x$'s combine for a final answer of:

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

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Example Question #31 : Distributive Property

Expand and combine like terms.

$\displaystyle (x-2)(x+10)$

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Using the FOIL distribution method:

$\displaystyle (x-2)(x+10)$

First: $\displaystyle x*x = x^2$

Outer: $\displaystyle x*10= 10x$

Inner: $\displaystyle -2*x = -2x$

Last: $\displaystyle -2*10=-20$

Resulting in: $\displaystyle x^2 +10x-2x-20$

Combining like terms, the $\displaystyle x$'s combine for a final answer of:

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

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Example Question #4844 : 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.

$\displaystyle 52*52=(50+2)(50+2)$

Possible Answers:

2504 $\displaystyle 2504$

2704 $\displaystyle 2704$

249 8 $\displaystyle 249 8$

2496 $\displaystyle 2496$

104 $\displaystyle 104$

Correct answer:

2704 $\displaystyle 2704$

Explanation:

Using the FOIL distribution method:

$\displaystyle (50+2)(50+2)$

First: $\displaystyle 50*50 = 2500$

Outer: $\displaystyle 50*2= 100$

Inner: $\displaystyle 2*50 = 100$

Last: 2*2=4 $\displaystyle 2*2=4$

Resulting in: $\displaystyle 2500 + 100 +100 +4 = 2704$

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Example Question #32 : 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.

$\displaystyle 33*44=(30+3)(40+4)$

Possible Answers:

1512 $\displaystyle 1512$

1212 $\displaystyle 1212$

1200 $\displaystyle 1200$

1452 $\displaystyle 1452$

252 $\displaystyle 252$

Correct answer:

1452 $\displaystyle 1452$

Explanation:

Using the FOIL distribution method:

$\displaystyle (30+3)(40+4)$

First: $\displaystyle 30*40 = 1200$

Outer: $\displaystyle 30*4= 120$

Inner: $\displaystyle 3*40 = 120$

Last: 3*4=12 $\displaystyle 3*4=12$

Resulting in: $\displaystyle 1200 + 120 +120 +12 = 1452$

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Example Question #33 : Distributive Property

Expand and simplify.

$\displaystyle (5x + t)(2x + 3t)$

Possible Answers:

$\displaystyle 10x^2 + 17x + 3t$

$\displaystyle x^2 + 7x + 4$

$\displaystyle 10x^2 + 17xt + 3t^2$

$\displaystyle x^2 + 5xt + 3t^2$

$\displaystyle 10x^2 + 13xt + 3t^2$

Correct answer:

$\displaystyle 10x^2 + 17xt + 3t^2$

Explanation:

Using the FOIL distribution method:

$\displaystyle (5x + t)(2x + 3t)$

First: $\displaystyle 5x*2x = 10x^2$

Outer: $\displaystyle 5x*3t= 15x t$

Inner: $\displaystyle t*2x = 2xt$

Last: $\displaystyle t*3t=3t^2$

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

Combining like terms, the $\displaystyle xt$'s combine for a final answer of:

$\displaystyle 10x^2 + 17xt + 3t^2$

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Example Question #34 : Distributive Property

Expand and simplify.

$\displaystyle (x + y)(x - y)$

Possible Answers:

$\displaystyle x^2 -2xy + y^2$

$\displaystyle x^2 +2xy + y^2$

$\displaystyle x^2 + y^2$

$\displaystyle x^2 +xy- y^2$

$\displaystyle x^2 - y^2$

Correct answer:

$\displaystyle x^2 - y^2$

Explanation:

Using the FOIL distribution method:

$\displaystyle (x + y)(x - y)$

First: $\displaystyle x*x = x^2$

Outer: $\displaystyle x*-y= -xy$

Inner: $\displaystyle y*x = xy$

Last: $\displaystyle y*-y=-y^2$

Resulting in: $\displaystyle x^2 - xy + xy - y^2$

Combining like terms, the $\displaystyle xy$'s cancel for a final answer of:

$\displaystyle x^2 - y^2$

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 #32 : Distributive Property

Expand by FOILing:

$\displaystyle (x+7)(x-2)$

Possible Answers:

$\displaystyle x^2-9x-14$

$\displaystyle x^2-5x-14$

$\displaystyle x^2+5x-14$

$\displaystyle x^2+9x-14$

Correct answer:

$\displaystyle x^2+5x-14$

Explanation:

First: $\displaystyle (x)(x)=x^2$

Outside: $\displaystyle (x)(-2)=-2x$

Inside: $\displaystyle (x)(7)=7x$

Last: $\displaystyle (-2)(7)=-14$

Add the values together and combine like terms:

$\displaystyle x^2-2x+7x-14=x^2+5x-14$

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Algebra 1 : Distributive Property

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #31 : Distributive Property

Example Question #32 : Distributive Property

Example Question #4844 : Algebra 1

Example Question #31 : Distributive Property

Example Question #31 : Distributive Property

Example Question #4844 : Algebra 1

Example Question #32 : Distributive Property

Example Question #33 : Distributive Property

Example Question #34 : Distributive Property

Example Question #32 : Distributive Property

All Algebra 1 Resources

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