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ACT Math : Distributive Property

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Example Questions

Example Question #41 : Distributive Property

$\displaystyle (2x+3)(10x-2)=$

Possible Answers:

$\displaystyle 20x^2+26x-6$

$\displaystyle 20x^2-26x-6$

$\displaystyle 10x^2+26x-6$

$\displaystyle 10x^2+26x+6$

Correct answer:

$\displaystyle 20x^2+26x-6$

Explanation:

Use the distributive property to FOIL.

$\displaystyle 20x^2-4x+30x-6$

$\displaystyle =20x^2+26x-6$

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Example Question #42 : Distributive Property

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

Possible Answers:

$\displaystyle y^2-xy-xz+yz$

$\displaystyle y+xy+xz+yz$

$\displaystyle y^2+xy+xz+yz$

$\displaystyle y^2+xy+xz-yz$

Correct answer:

$\displaystyle y^2+xy+xz+yz$

Explanation:

FOIL using the distributive property.

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

$\displaystyle =y^2+xy+xz+yz$

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Example Question #43 : Distributive Property

$\displaystyle (3x-5)(x+3)$

Possible Answers:

$\displaystyle x^2+4x-15$

$\displaystyle 3x^2+4x-15$

$\displaystyle 3x^2-4x-15$

$\displaystyle 3x^2+4x+15$

Correct answer:

$\displaystyle 3x^2+4x-15$

Explanation:

Use the distributive property to FOIL.

$\displaystyle 3x^2+9x-5x-15$

Simplify.

$\displaystyle 3x^2+4x-15$

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Example Question #44 : Distributive Property

Use FOIL to expand

$\displaystyle (x+2)(x-5)$

Possible Answers:

$\displaystyle x^2-3x-10$

x-3 $\displaystyle x-3$

x^2-10 $\displaystyle x^2-10$

$\displaystyle x^2+3x-10$

Correct answer:

$\displaystyle x^2-3x-10$

Explanation:

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

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

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Example Question #41 : Foil

FOIL the following:

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

Possible Answers:

x^2-x-6 $\displaystyle x^2-x-6$

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

x^2-x+6 $\displaystyle x^2-x+6$

x^2+x-6 $\displaystyle x^2+x-6$

Correct answer:

x^2+x-6 $\displaystyle x^2+x-6$

Explanation:

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

Thus, perform the following multiplication.

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

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

Outside: $x\cdot 3=3x$ $\displaystyle x\cdot 3=3x$

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

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

Gathering like terms results in the final equation.

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

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Example Question #1141 : Algebra

What is $\displaystyle (2x-3)(2x+3)$ ?

Possible Answers:

$\displaystyle 9x^2 - 4$

$\displaystyle 3x^2 - 6$

$\displaystyle 6x^2 - 6$

$\displaystyle 6x^2 - 3$

$\displaystyle 4x^2 - 9$

Correct answer:

$\displaystyle 4x^2 - 9$

Explanation:

The simple formula for difference of two squares is:

$\displaystyle (2x-3)(2x+3) = 2^2 x^2 - 3^2$ .

To see this, you can also FOIL out

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

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

$\displaystyle 4x^2 + 6x - 6x - 9 =$

Gathering like terms the x's cancel out.

$\displaystyle 4x^2 - 9$

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Example Question #1142 : Algebra

What is $\displaystyle (-3x+1)(-3x-1)$ ?

Possible Answers:

$\displaystyle 9x^2 + 1$

$\displaystyle 9x^2 - 1$

$\displaystyle 3x^2 - 9$

$\displaystyle -9x^2 + 1$

$\displaystyle -9x^2 - 1$

Correct answer:

$\displaystyle 9x^2 - 1$

Explanation:

Diffference of two squares formula,

$\displaystyle (-3x+1)(-3x-1) =$

$\displaystyle (-3x)^2 - (1)^2 =$

$\displaystyle 9x^2 - 1$

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

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

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

$\displaystyle 9x^2 + 3x - 3x - 1 =$

$\displaystyle 9x^2 - 1$

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Example Question #45 : Distributive Property

Multiply the complex numbers:

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

Possible Answers:

$22+32i$ $\displaystyle 22+32i$

$-24+30i$ $\displaystyle -24+30i$

$-26-32i$ $\displaystyle -26-32i$

$26+32i$ $\displaystyle 26+32i$

$-26+32i$ $\displaystyle -26+32i$

Correct answer:

$-26+32i$ $\displaystyle -26+32i$

Explanation:

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

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

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Example Question #1142 : Algebra

Solve for $\displaystyle x$ .

$\displaystyle 7x = -3(4-x)$

Possible Answers:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\displaystyle -3$

$\displaystyle 3$

$\frac{6}{5}$ $\displaystyle \frac{6}{5}$

$\frac{3}{2}$ $\displaystyle \frac{3}{2}$

Correct answer:

$\displaystyle -3$

Explanation:

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

$\displaystyle 7x = -12+3x$

Then, subtract $\displaystyle 3x$ from both sides.

4x=-12 $\displaystyle 4x=-12$

Then divide both sides by $\displaystyle 4$ .

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

x=-3 $\displaystyle x=-3$

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

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Example Question #1141 : Algebra

$\displaystyle (x+y)(x+2y)=$

Possible Answers:

$\displaystyle x^2+4xy+2y^2$

$\displaystyle x^2+3xy+2y^2$

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

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

Correct answer:

$\displaystyle x^2+3xy+2y^2$

Explanation:

FOIL by using the distributive property.

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

Now, simplify.

$\displaystyle x^2+3xy+2y^2$

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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 : Distributive Property

Example Question #42 : Distributive Property

Example Question #43 : Distributive Property

Example Question #44 : Distributive Property

Example Question #41 : Foil

Example Question #1141 : Algebra

Example Question #1142 : Algebra

Example Question #45 : Distributive Property

Example Question #1142 : Algebra

Example Question #1141 : Algebra

All ACT Math Resources

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