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