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

The solution to expand (3d-5e)(9d^2-15de+25e^2) is 27d^3-90ed^2+150e^2d-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} - 90 e d^{2} + 150 e^{2} d - 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 (- 15 d e) + 3 d \cdot 25 e^{2} + (- 5 e) \cdot 9 d^{2} + (- 5 e) (- 15 d e) + (- 5 e) \cdot 25 e^{2}

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= 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} - 90 e d^{2} + 150 e^{2} d - 125 e^{3}

= 27 d^{3} - 90 e d^{2} + 150 e^{2} d - 125 e^{3}

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

\frac{4 \cdot ( t - 10 ) ^{2}}{375}

x 5 y 3

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

2 x + 3 - (x + 1) e^{x}

What is expand (3d-5e)(9d^2-15de+25e^2) ?
The solution to expand (3d-5e)(9d^2-15de+25e^2) is 27d^3-90ed^2+150e^2d-125e^3