Question

what is a factor of the expression 250 x cubed - 16 y ^ 3

Answer 1

Consider the given expression as,

$250x^3-16y^3$

The equation can be written as,

$(\sqrt[3]{250}x)^3-(\sqrt[3]{16}y)^3$

Use the algebraic identity,

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

Substitute the values and simplify,

$(\sqrt[3]{250}x)^3-(\sqrt[3]{16}y)^3=(\sqrt[3]{250}x-\sqrt[3]{16}y)\mleft\lbrace(\sqrt[3]{250}x)^2+(\sqrt[3]{250}x)(\sqrt[3]{16}y)+(\sqrt[3]{16}y)^2\mright\rbrace$

Thus, the factors of the given expression are,

$(\sqrt[3]{250}x-\sqrt[3]{16}y)\text{ and }\lbrace(\sqrt[3]{250}x)^2\text{ and }(\sqrt[3]{250}x)(\sqrt[3]{16}y)+(\sqrt[3]{16}y)^2\rbrace$