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ACT Math : Distributive Property

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Example Questions

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Example Question #41 : How To Use Foil With The Distributive Property

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

Possible Answers:

10x^2+26x-6

10x^2+26x+6

20x^2-26x-6

20x^2+26x-6

Correct answer:

20x^2+26x-6

Explanation:

Use the distributive property to FOIL.

20x^2-4x+30x-6

=20x^2+26x-6

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Example Question #42 : How To Use Foil With The Distributive Property

(x+y)(y+z)

Possible Answers:

y^2-xy-xz+yz

y^2+xy+xz-yz

y^2+xy+xz+yz

y+xy+xz+yz

Correct answer:

y^2+xy+xz+yz

Explanation:

FOIL using the distributive property.

(x+y)(y+z)=xy+xz+y^2+yz

=y^2+xy+xz+yz

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Example Question #43 : How To Use Foil With The Distributive Property

(3x-5)(x+3)

Possible Answers:

3x^2+4x+15

3x^2+4x-15

x^2+4x-15

3x^2-4x-15

Correct answer:

3x^2+4x-15

Explanation:

Use the distributive property to FOIL.

3x^2+9x-5x-15

Simplify.

3x^2+4x-15

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Example Question #44 : How To Use Foil With The Distributive Property

Use FOIL to expand

(x+2)(x-5)

Possible Answers:

x-3

x^2+3x-10

x^2-3x-10

x^2-10

Correct answer:

x^2-3x-10

Explanation:

To FOIL, simply multiply each term by each term in the other parenthesis. Thus,

x*x+x*(-5)+x*(2)+(-5)(2)=x^2-5x+2x-10=x^2-3x-10

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Example Question #45 : How To Use Foil With The Distributive Property

FOIL the following:

(x-2)(x+3)

Possible Answers:

x^2+5x-6

x^2+x-6

x^2-x-6

x^2-x+6

Correct answer:

x^2+x-6

Explanation:

To FOIL, remember the acronym. F-first, O-outside, I-inside, L-last.

Thus, perform the following multiplication.

(x-2)(x+3)

Firsts: $x\cdot x=x^2$

Outside: $x\cdot 3=3x$

Inside: $-2\cdot x=-2x$

Lasts: $-2\cdot 3=-6$

Gathering like terms results in the final equation.

$\\=x^2+3x-2x-6\\=x^2+x-6$

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Example Question #46 : How To Use Foil With The Distributive Property

What is (2x-3)(2x+3) ?

Possible Answers:

3x^2 - 6

9x^2 - 4

4x^2 - 9

6x^2 - 3

6x^2 - 6

Correct answer:

4x^2 - 9

Explanation:

The simple formula for difference of two squares is:

(2x-3)(2x+3) = 2^2 x^2 - 3^2 .

To see this, you can also FOIL out

(2x-3)(2x+3)=

Multiplying the first terms, outer terms, inner terms, and last terms results in the following.

4x^2 + 6x - 6x - 9 =

Gathering like terms the x's cancel out.

4x^2 - 9

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Example Question #47 : How To Use Foil With The Distributive Property

What is (-3x+1)(-3x-1) ?

Possible Answers:

9x^2 + 1

-9x^2 + 1

-9x^2 - 1

9x^2 - 1

3x^2 - 9

Correct answer:

9x^2 - 1

Explanation:

Diffference of two squares formula,

(-3x+1)(-3x-1) =

(-3x)^2 - (1)^2 =

9x^2 - 1

Note that (-3)^2 = 9 , negative cancels out.

You can also FOIL: (-3x+1)(-3x-1) =

Multiplying the first terms, outer terms, inner terms, and last terms results in the following.

9x^2 + 3x - 3x - 1 =

9x^2 - 1

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Example Question #45 : How To Use Foil With The Distributive Property

Multiply the complex numbers:

$(3+4i)(2+8i)$ .

Possible Answers:

$-24+30i$

$22+32i$

$-26+32i$

$26+32i$

$-26-32i$

Correct answer:

$-26+32i$

Explanation:

Expanding out gives $6+24i+8i+32i^{2}$ .

We know that $i=\sqrt{-1}$ so when we substitute that in we get $6+32i-32$ .

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Example Question #49 : How To Use Foil With The Distributive Property

Solve for .

7x = -3(4-x)

Possible Answers:

$\frac{3}{2}$

$\frac{6}{5}$

$\frac{1}{2}$

Correct answer:

Explanation:

To solve this equation, first distribute on the right side of the equation.

7x = -12+3x

Then, subtract from both sides.

4x=-12

Then divide both sides by .

$\frac{4x}{4}=\frac{-12}{4}$

x=-3

Another method for solving this problem is to plug in the answer choices and solve.

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Example Question #41 : Distributive Property

(x+y)(x+2y)=

Possible Answers:

x^2+2xy+2y^2

x^2+xy+2y^2

x^2+4xy+2y^2

x^2+3xy+2y^2

Correct answer:

x^2+3xy+2y^2

Explanation:

FOIL by using the distributive property.

x^2+2xy+xy+2y^2

Now, simplify.

x^2+3xy+2y^2

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ACT Math : Distributive Property

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #41 : How To Use Foil With The Distributive Property

Example Question #42 : How To Use Foil With The Distributive Property

Example Question #43 : How To Use Foil With The Distributive Property

Example Question #44 : How To Use Foil With The Distributive Property

Example Question #45 : How To Use Foil With The Distributive Property

Example Question #46 : How To Use Foil With The Distributive Property

Example Question #47 : How To Use Foil With The Distributive Property

Example Question #45 : How To Use Foil With The Distributive Property

Example Question #49 : How To Use Foil With The Distributive Property

Example Question #41 : Distributive Property

All ACT Math Resources

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