What's the expression of this?

Question

asked Dec 6, 2024 180k views

1 Answer

Dyana · Answer 1 · 2024-12-11T17:34:42+0000

Answer:

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

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

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

If you have any questions tag me on comments

Hope it helps!!!