Question

6. Fatore os binômios dados.
a)x^3-1/8
b)x^3/27+64

Answer 1

Fatoração soma de cubos

$\large\boxed{\boxed{\boxed{\boxed{\mathsf{a^3+b^3=(a+b)(a^2-ab+b^2)}}}}}$

Fatoração da diferença

de cubos

$\large\boxed{\boxed{\boxed{\boxed{\mathsf{a^3-b^3=(a-b)(a^2+ab+b^2)}}}}}$

$\dotfill$

$\mathtt{a)}~\large\boxed{\boxed{\boxed{\boxed{\mathsf{x^3-\dfrac{1}{8}=(x-\dfrac{1}{2})(x^2+\dfrac{1}{2}x+\dfrac{1}{4}}}}}}\\\mathtt{b)}\\ \large\boxed{\boxed{\boxed{\boxed{\mathsf{\dfrac{x^3}{27}+64=(\dfrac{x}{3}+4)(\dfrac{x^2}{9}-\dfrac{4}{3}x+16)}}}}}$