What is expand (3e^2-5f)^3 ?

The solution to expand (3e^2-5f)^3 is -125f^3+225e^2f^2-135e^4f+27e^6

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expand (3e^2-5f)^3

expand

(3 e^{2} - 5 f)^{3}

- 125 f^{3} + 225 e^{2} f^{2} - 135 e^{4} f + 27 e^{6}

Solution steps

(3 e^{2} - 5 f)^{3}

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

a = 3 e^{2}, b = 5 f

= (3 e^{2})^{3} - 3 (3 e^{2})^{2} \cdot 5 f + 3 \cdot 3 e^{2} (5 f)^{2} - (5 f)^{3}

Simplify

(3 e^{2})^{3} - 3 (3 e^{2})^{2} \cdot 5 f + 3 \cdot 3 e^{2} (5 f)^{2} - (5 f)^{3} : 27 e^{6} - 135 e^{4} f + 225 e^{2} f^{2} - 125 f^{3}

= 27 e^{6} - 135 e^{4} f + 225 e^{2} f^{2} - 125 f^{3}

Rewrite in standard form

= - 125 f^{3} + 225 e^{2} f^{2} - 135 e^{4} f + 27 e^{6}

\frac{( a + b ) ^{2}}{a ^{2} + b ^{2}}

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\frac{x ^{2} - 3 x + 10}{( 3 - x ) x ^{2}}

\frac{( 1 + 6 x )}{( ( 4 x - 3 ) ( 2 x + 5 ) )}

What is expand (3e^2-5f)^3 ?
The solution to expand (3e^2-5f)^3 is -125f^3+225e^2f^2-135e^4f+27e^6