Question

Factor 125x^3+216y^3 in descending order

Answer 1

Hello!

The answer is: $(5x+6y)(25x^{2}-30xy+36y^{2})$

Why?

If we have:

$a^{3}+b^{3}$

We can factor it by the following way:

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

So,

we have that:

$a=\sqrt[3]{125}=25\\b=\sqrt[3]{216}=6$

So, factoring we have:

$125x^{3}+216y^{3}=(5x)^{3}+(6y)^{3}\\(5x+6y)(25x^{2}-30xy+36y^{2})$

Let's prove that we are right:

$(5x+6y)(25x^{2}-30xy+36y^{2})=125x^{3}-150x^{2}y+180xy^{2}+150x^{2}y-180xy^{2}+216y^{3}=125x^{3}+216y^{3}$

Have a nice day!

Answer 2

Answer:

see explanation

Step-by-step explanation:

This is a sum of cubes and factors in general as

a³ + b³ = (a + b)(a² - ab + b²)

125x³ = (5x)³ ⇒ a = 5x

216y³ = (6y)³ ⇒ b = 6y

Hence

125x³ + 216y³

= (5x + 6y)((5x)² - (5x)(6y) + (6y)²) = (5x + 6y)(25x² - 30xy + 36y²)