Question

Hello Factor this with steps please

Answer 1

`(2x-3)(4x^2+6x+9)`

Explanation:

Given expression:

`8x^3-27`

Rewrite 8 as 2³ and 27 as 3³:

`\implies 2^3 \cdot x^3-3^3`

`\textsf{Apply exponent rule} \quad a^b \cdot c^b=(ac)^b`

`\implies (2x)^3-3^3`

`\boxed{\begin{minipage}{5cm}\underline{Difference of Cubes Formula}\\\\$a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)$\\\end{minipage}}`

Apply the Difference of Cubes Formula.

Therefore:

• a = 2x
• b = 3

`\implies (2x-3)((2x)^2+2x \cdot 3+3^2)`

`\implies (2x-3)(4x^2+6x+9)`