Question

Simplify this
27x^3-8/3x-2

Answer 1

Answer:

$the \: answer \: of \: this \: question \: is9 {x}^{2} + 6x + 4$

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Answer 2

Answer:

$\boxed{9x^2+6x+4}$

Step-by-step explanation:

Distributive property: a(b+c)=ab+ac

$\frac{27x^3-8}{3x-2}$

Factor.

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

Rewrite the problem down.

$27x^3-8=(3x)^3-2^3$

$(3x^3)-2^3$

Cubes formula: ⇒ $x^3-y^3=(x-y)(x^2+xy+y^2)$

$(3x)^3-2^3=(3x-2)(3^2x^2+2*3x+2^2)=9x^2+6x+4$

$\frac{(3x-2)(9x^2+6x+4)}{3x-2}=9x^2+6x+4$

Cancel by the common factor of 3x-2.

$9x^2+6x+4\checkmark$

$9x^2+6x+4$, which is correct answer.