Answer :

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)

mixter17

Hello!

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

Why?

If we have:

[tex]a^{3}+b^{3}[/tex]

We can factor it by the following way:

[tex]a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})[/tex]

So,

we have that:

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

So, factoring we have:

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

Let's prove that we are right:

[tex](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}[/tex]

Have a nice day!

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