What is expand (3d-5e)(9d^2+15de+25e^2) ?

The solution to expand (3d-5e)(9d^2+15de+25e^2) is 27d^3-125e^3

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expand (3d-5e)(9d^2+15de+25e^2)

expand

(3 d - 5 e) (9 d^{2} + 15 d e + 25 e^{2})

27 d^{3} - 125 e^{3}

Solution steps

(3 d - 5 e) (9 d^{2} + 15 d e + 25 e^{2})

= (3 d - 5 e) (9 d^{2} + 15 e d + 25 e^{2})

Distribute parentheses

= 3 d \cdot 9 d^{2} + 3 d \cdot 15 d e + 3 d \cdot 25 e^{2} + (- 5 e) \cdot 9 d^{2} + (- 5 e) \cdot 15 d e + (- 5 e) \cdot 25 e^{2}

Apply minus-plus rules

+ (- a) = - a

= 3 \cdot 9 d^{2} d + 3 \cdot 15 e dd + 3 \cdot 25 e^{2} d - 5 \cdot 9 e d^{2} - 5 \cdot 15 ee d - 5 \cdot 25 e^{2} e

Simplify

3 \cdot 9 d^{2} d + 3 \cdot 15 e dd + 3 \cdot 25 e^{2} d - 5 \cdot 9 e d^{2} - 5 \cdot 15 ee d - 5 \cdot 25 e^{2} e : 27 d^{3} - 125 e^{3}

= 27 d^{3} - 125 e^{3}

sin ((2 n - 1) π)

\frac{x ^{2} ( x + 4 )}{( x - 1 ) ( x + 2 )}

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

\frac{s ^{2} - 25}{( s ^{2} + 25 ) ^{2}}

\frac{5 ( k + 1 ) ( k + 2 )}{2}

What is expand (3d-5e)(9d^2+15de+25e^2) ?
The solution to expand (3d-5e)(9d^2+15de+25e^2) is 27d^3-125e^3