Question

What's the expression of this?

Answer 1

`(3m + 5n)(9m {}^(2) - 15mn + 25n {}^(2) )`

Explanation:

Greetings!!!

Given expression

`27m {}^(3) + 125n {}^(3)`

Apply exponents rule

Rewrite 27 as 3³

`= 3 {}^(3) m {}^(3) + 125n {}^(3)`

Rewrite 125 as 5³

`= 3 {}^(3) m {}^(3) + 5 {}^(3) n {}^(3)`

Apply exponent rule:

`a {}^(m) b {}^(m) = (ab) {}^(m) \\ = 3 {}^(3) m {}^(3) = (3m) {}^(3) \\ = 5 {}^(3) n {}^(3) = (5n) {}^(3)`

Apply sum of cubes formula

`x {}^(3) + y {}^(3) = (x + y) (x {}^(2) - xy + y {}^(2) )`

`(3m {}^(3)) + (5n {}^(3) ) = (3m + 5n)((3m) {}^(2) - 3m.5n + (5n {}^){2} ) \\ = (3m + 5n)((3m {}^(2) ) - 3m.5n + (5n {}^(2) ))`

simplify

`= (3m + 5n)(9m {}^(2) - 15mn + 25n {}^(2) )`

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Hope it helps!!!