What is expand (2d+5e)(4d^2-10de+25e^2) ?

The solution to expand (2d+5e)(4d^2-10de+25e^2) is 8d^3+125e^3

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expand (2d+5e)(4d^2-10de+25e^2)

expand

(2 d + 5 e) (4 d^{2} - 10 d e + 25 e^{2})

8 d^{3} + 125 e^{3}

Solution steps

(2 d + 5 e) (4 d^{2} - 10 d e + 25 e^{2})

= (2 d + 5 e) (4 d^{2} - 10 e d + 25 e^{2})

Distribute parentheses

= 2 d \cdot 4 d^{2} + 2 d (- 10 d e) + 2 d \cdot 25 e^{2} + 5 e 4 d^{2} + 5 e (- 10 d e) + 5 e 25 e^{2}

Apply minus-plus rules

+ (- a) = - a

= 2 \cdot 4 d^{2} d - 2 \cdot 10 e dd + 2 \cdot 25 e^{2} d + 5 \cdot 4 e d^{2} - 5 \cdot 10 ee d + 5 \cdot 25 e^{2} e

Simplify

2 \cdot 4 d^{2} d - 2 \cdot 10 e dd + 2 \cdot 25 e^{2} d + 5 \cdot 4 e d^{2} - 5 \cdot 10 ee d + 5 \cdot 25 e^{2} e : 8 d^{3} + 125 e^{3}

= 8 d^{3} + 125 e^{3}

\frac{( x - 7 ) ( x - 2 )}{( x + 2 ) ( x - 1 ) ^{2}}

\frac{3}{4} (1 + s) (1 - t) + \frac{5}{4} (1 + s) (1 + t)

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

(3 x - 8 y - 18 = 0,) (3 x - 8 y + 1 = 0)

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

What is expand (2d+5e)(4d^2-10de+25e^2) ?
The solution to expand (2d+5e)(4d^2-10de+25e^2) is 8d^3+125e^3