Question

Drag the factors to the correct locations on the image. Not all factors will be used.

What is the factored form of this expression?
27m³ + 125n³
9m+25n 3m+ 5n
9m² 15mn + 25n²
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(
3m
3m²
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5n
8mn + 5n²
X
9m² + 15mn + 25n²
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)

Answer 1

(3m + 5n)(9m² - 15mn + 25n²)

Explanation:

Algebraic Identity:

`\sf \boxed{\bf a^3 +b^3= (a +b)(a^2 - ab + b^2)}`

27 = 3 * 3 *3 = 3³

125 = 5 * 5 * 5 = 5³

27m³ + 125n³ = (3m)³ + (5n)³ {a = 3m & b = 5n}

= (3m + 5n)( (3m)² - 3m *5n + (5n)² )

=( 3m + 5n)(9m² - 15mn + 25n²)