FOIL

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ACT Math › FOIL

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

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.

3

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 $6+32i-32$ .

4

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:

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

5

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 $6+32i-32$ .

6

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:

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

7

The expression is equivalent to .

Explanation

This question is asking you to multiply two binomials. You can use the grid method for FOIL.

Foil

8

The expression is equivalent to .

Explanation

This question is asking you to multiply two binomials. You can use the grid method for FOIL.

Foil

9

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.

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

10

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.

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

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