Question

7.
Which is a factored form of 8x³ + 27? (1 point)
O (2x+3)(2x+3)(2x + 3)
O (2x+3)(4x² – 6x +9)
○ (2x − 3)(4x² + 6x + 9)
O(2x-9)(4x² + 18x +81)

Answers

  1. Answer:
    • B) (2x + 3)(4x² – 6x + 9)
    ———————————–
    Given sum of cubes, use identity a³ + b³ = (a + b)(a² – ab + b²):
    • 8x³ + 27 =
    • (2x)³ + 3³ =
    • (2x + 3)((2x)² – (2x)(3) + 3²) =
    • (2x + 3)(4x² – 6x + 9)
    The matching choice is B.

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  2. Answer:
    B)  (2x + 3)(4x² – 6x + 9)
    Step-by-step explanation:
    Given expression:
    8x^3+27
    Rewrite  8 as 2³  and  27 as 3³:
    \implies 2^3x^3+3^3
    \textsf{Apply exponent rule} \quad a^nc^n=(ac)^n:
    \implies (2x)^3+3^3
    \boxed{\begin{minipage}{5 cm}\underline{Sum of Cubes Formula}\\\\$a^3+b^3=(a+b)(a^2-ab+b^2)\\\end{minipage}}
    Therefore:
    • a = 2x
    • b = 3
    Using the Sum of Cubes formula:
    \begin{aligned}\implies (2x)^2+3^3&=(2x+3)((2x)^2-2x(3)+3^2)\\&=(2x+3)(4x^2-6x+9)\end{aligned}

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