Question

Разложите на множители выражение ​

Answer 1

Ответ:

$\Gamma ) \bigg (\dfrac{y}{4}-0,3x^{2} \bigg ) \bigg (\dfrac{y^{2}}{16}+\dfrac{3}{40}x^{2}y+0,09x^{4} \bigg )$

Пошаговое объяснение:

$a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2});$

$-0,027x^{6}+\dfrac{y^{3}}{64}=\dfrac{-27}{1000}x^{6}+\dfrac{y^{3}}{4^{3}}=\dfrac{(-3)^{3}}{10^{3}} \cdot x^{2 \cdot 3}+\bigg (\dfrac{y}{4} \bigg )^{3}=\bigg (\dfrac{-3}{10} \bigg )^{3} \cdot (x^{2})^{3}+\bigg (\dfrac{y}{4} \bigg )^{3}=$

$=\bigg (\dfrac{y}{4} \bigg )^{3}+(-1)^{3} \cdot (0,3)^{3} \cdot (x^{2})^{3}=\bigg (\dfrac{y}{4} \bigg )^{3}-(0,3x^{2})^{3}=\bigg (\dfrac{y}{4}-0,3x^{2} \bigg ) \bigg (\bigg (\dfrac{y}{4} \bigg )^{2}+$

$+\dfrac{y}{4} \cdot 0,3x^{2}+(0,3x^{2})^{2} \bigg )=\bigg (\dfrac{y}{4}-0,3x^{2} \bigg ) \bigg (\dfrac{y^{2}}{4^{2}}+\dfrac{0,3}{4}x^{2}y+(0,3)^{2} \cdot (x^{2})^{2} \bigg )=$

$=\bigg (\dfrac{y}{4}-0,3x^{2} \bigg ) \bigg (\dfrac{y^{2}}{16}+\dfrac{3}{40}x^{2}y+0,09x^{4} \bigg );$