How to use FOIL with the distributive property

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ACT Math › How to use FOIL with the distributive property

Questions 1 - 10

1

For all x, (4_x –_ 3)2 =

12_x_2 + 24_x –_ 9

16_x_2 – 9

16_x_2 + 9

16_x_2 + 24_x_ + 9

16_x_2 – 24_x_ + 9

Explanation

To solve this problem, you should FOIL: (4_x_ – 3)(4_x_ – 3) = 16_x_2 – 12_x –_ 12_x_ + 9 = 16_x_2 – 24_x_ + 9.

2

Multiply the complex numbers:

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

$-26+32i$

$-24+30i$

$26+32i$

$-26-32i$

$22+32i$

Explanation

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

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

3

Expand the following expression:

$(2x)(x+1)^{2}$

$x^{2}+2x+1$

$x^{3}+4x^{2}+2x$

$2x^{3}+4x^{2}+2x$

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

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

Explanation

FOIL $(x+1)^{2}$ and we get:

$(x^{2}+2x+1)$

Then multiply it by and get:

$(2x^{3}+4x^{2}+2x)$

4

FOIL the following:

Explanation

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

Thus, perform the following multiplication.

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.

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

5

Distribute:

Explanation

Use the distributive property to FOIL

Simplify.

6

FOIL:

Explanation

By FOIL (First Outer Inner Last), we obtain –8_x_2 – 8_x_ – 6_x_ – 6.

Simplify: –8_x_2 – 14_x_ – 6

7

Which of the following is equivalent to (2g – 3h)2?

g2 – 12gh + 9h2

4g2 – 12gh + 3h2

4g2 – 12gh + 9h2

4g2 – 6gh + 9h2

4g2 + 9h2

Explanation

Use FOIL: (2g – 3h)(2g – 3h) = 4g2 – 6gh – 6gh + 9h2 = 4g2 – 12gh + 9h2

8

What is the product of the two real solutions of x2 + 5x = 6?

**–**6

6

1

**–**1

Explanation

x2 + 5x – 6 = 0 factors to (x+6)(x**–**1) = 0.

Therefore, the two real solutions are x = **–**6 and x = 1. Their product is simply **–**6.

9

Expand the following expression:

(B – 2) (B + 4)

B2 + 2B – 8

B2 – 2B – 8

B2 + 4B – 8

B2 – 4B – 8

B2 + 2B + 8

Explanation

Here we use FOIL:

Firsts: B * B = B2

Outer: B * 4 = 4B

Inner: –2 * B = –2B

Lasts: –2 * 4 = –8

All together this yields

B2 + 2B – 8

10

A rectangle's length L is 3 inches shorter than its width, W. What is an appropriate expression for the area of the rectangle in terms of W?

2W – 3

W2 – 3

W2 – 3W

2W2 – 3

2W2 – 3W

Explanation

The length is equal to W – 3

The area of a rectangle is length x width.

So W * (W – 3) = W2 – 3W

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