Question

① $x^3 - 8$
② $8a^3 - 27$

Explanation:

Step1: Identify difference of cubes

For $x^3 - 8$: $x^3 = (x)^3$, $8 = 2^3$.
Use formula $a^3 - b^3=(a-b)(a^2+ab+b^2)$

Step2: Substitute values for first expression

Let $a=x$, $b=2$.
$x^3 - 8=(x-2)(x^2 + 2x + 2^2)=(x-2)(x^2+2x+4)$

Step3: Identify difference of cubes

For $8a^3 - 27$: $8a^3=(2a)^3$, $27=3^3$.
Use formula $a^3 - b^3=(a-b)(a^2+ab+b^2)$

Step4: Substitute values for second expression

Let $a=2a$, $b=3$.
$8a^3 - 27=(2a-3)((2a)^2+(2a)(3)+3^2)=(2a-3)(4a^2+6a+9)$

Answer:

1. $(x-2)(x^2+2x+4)$
2. $(2a-3)(4a^2+6a+9)$