Question

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

Answer 1

see explanation

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)

Answer 2

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!