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)

Answer 1

B) (2x + 3)(4x² - 6x + 9)

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}`

Answer 2

• 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.