Question

1. match the polynomial with its factored form.

$a^3 - b^3$
$a^3 + b^3$
$a^2 - b^2$
$a^2 + 2ab + b^2$
$a^2 - 2ab + b^2$

a. $(a - b)(a - b)$
b. $(a + b)(a - b)$
c. $(a + b)(a^2 - ab + b^2)$
d. $(a - b)(a^2 + ab + b^2)$
e. $(a + b)(a + b)$

1. factor the polynomials.

$x^3 - 27$

$\bigcirc$ $(x - 3)(x^2 + 3x - 9)$
$\bigcirc$ $(x - 3)(x^2 - 3x - 9)$
$\bigcirc$ $(x - 3)(x^2 + 3x + 9)$
$\bigcirc$ $(x - 3)(x^2 - 3x + 9)$

Explanation:

For Question 4:

Step1: Match difference of cubes

$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ (matches d)

Step2: Match sum of cubes

$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ (matches c)

Step3: Match difference of squares

$a^2 - b^2 = (a + b)(a - b)$ (matches b)

Step4: Match perfect square sum

$a^2 + 2ab + b^2 = (a + b)(a + b)$ (matches e)

Step5: Match perfect square difference

$a^2 - 2ab + b^2 = (a - b)(a - b)$ (matches a)

Step1: Recognize difference of cubes

$x^3 - 27 = x^3 - 3^3$

Step2: Apply difference of cubes formula

Use $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$, where $a=x$, $b=3$
$x^3 - 3^3 = (x - 3)(x^2 + 3x + 9)$

Answer:

• $a^3 - b^3$ : d. $(a - b)(a^2 + ab + b^2)$
• $a^3 + b^3$ : c. $(a + b)(a^2 - ab + b^2)$
• $a^2 - b^2$ : b. $(a + b)(a - b)$
• $a^2 + 2ab + b^2$ : e. $(a + b)(a + b)$
• $a^2 - 2ab + b^2$ : a. $(a - b)(a - b)$

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For Question 5: