Question

5
drag the factors to the correct locations on the image. not all factors will be used.
what is the factored form of this expression?
$27m^3 + 125n^3$
$9m^2 + 15mn + 25n^2$ $5n$ $3m^2 - 8mn + 9m^2 - 15mn + 25n^2$ $5n$
$9m + 25n$
$(\quad)(\quad)$

Explanation:

Step1: Identify the formula

The expression \(27m^3 + 125n^3\) is a sum of cubes. The formula for factoring a sum of cubes is \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\).
Here, \(a^3 = 27m^3\), so \(a=\sqrt[3]{27m^3}=3m\). And \(b^3 = 125n^3\), so \(b=\sqrt[3]{125n^3}=5n\).

Step2: Apply the formula

Substitute \(a = 3m\) and \(b = 5n\) into the sum of cubes formula.
First, \(a + b=3m + 5n\).
Then, \(a^2 - ab + b^2=(3m)^2-(3m)(5n)+(5n)^2 = 9m^2-15mn + 25n^2\).

Answer:

\((3m + 5n)(9m^2 - 15mn + 25n^2)\)