Question

directions: foil each expression.

1. $(2x - 1)(2x - 1)$
2. $(2x - 1)(2x + 1)$
3. $(x + 4)(x - 2)$
4. $(2x - 1)(3x + 4)$
5. $(10 - x)(8 + x)$
6. $(- x + 21)(x + 2)$
7. indicate whether each number is rational or irrational.

0.45 $square$ rational $square$ irr
$pi$ $square$ rational $square$ irr
$sqrt{2}$ $square$ rational $square$ in
$square$ rational $square$ in

Explanation:

Step1: FOIL (First, Outer, Inner, Last)

$(2x)(2x) + (2x)(-1) + (-1)(2x) + (-1)(-1)$

Step2: Simplify terms

$4x^2 - 2x - 2x + 1$

Step3: Combine like terms

$4x^2 - 4x + 1$

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Step1: FOIL the binomials

$(2x)(2x) + (2x)(1) + (-1)(2x) + (-1)(1)$

Step2: Simplify terms

$4x^2 + 2x - 2x - 1$

Step3: Combine like terms

$4x^2 - 1$

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Step1: FOIL the binomials

$(x)(x) + (x)(-2) + (4)(x) + (4)(-2)$

Step2: Simplify terms

$x^2 - 2x + 4x - 8$

Step3: Combine like terms

$x^2 + 2x - 8$

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Step1: FOIL the binomials

$(2x)(3x) + (2x)(4) + (-1)(3x) + (-1)(4)$

Step2: Simplify terms

$6x^2 + 8x - 3x - 4$

Step3: Combine like terms

$6x^2 + 5x - 4$

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Step1: FOIL the binomials

$(10)(8) + (10)(x) + (-x)(8) + (-x)(x)$

Step2: Simplify terms

$80 + 10x - 8x - x^2$

Step3: Combine like terms

$-x^2 + 2x + 80$

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Step1: FOIL the binomials

$(-x)(x) + (-x)(2) + (21)(x) + (21)(2)$

Step2: Simplify terms

$-x^2 - 2x + 21x + 42$

Step3: Combine like terms

$-x^2 + 19x + 42$

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Step1: Classify 0.45

0.45 is a terminating decimal, so it can be written as $\frac{45}{100}$, a ratio of integers.

Step2: Classify $\pi$

$\pi$ is a non-repeating, non-terminating decimal that cannot be written as a ratio of integers.

Step3: Classify $\sqrt{2}$

$\sqrt{2}$ is a non-repeating, non-terminating decimal that cannot be written as a ratio of integers.

Answer:

1. $4x^2 - 4x + 1$
2. $4x^2 - 1$
3. $x^2 + 2x - 8$
4. $6x^2 + 5x - 4$
5. $-x^2 + 2x + 80$
6. $-x^2 + 19x + 42$

7.

• 0.45: rational
• $\pi$: irrational
• $\sqrt{2}$: irrational