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Popular >

expand (b/a (x-d)-f-c)^3

Solution

expand

(\frac{b}{a} (x - d) - f - c)^{3}

Solution

\frac{b ^{3} ( x - d ) ( x - d ) ( x - d )}{a ^{3}} + \frac{- 3 b ^{2} x ^{2} f - 3 b ^{2} f d ^{2} - 3 b ^{2} x ^{2} c - 3 b ^{2} d ^{2} c + 2 b ^{2} d x f + 4 b ^{2} d c x + 2 d x b ^{2} f + 2 d c x b ^{2} + 2 x b ^{2} df}{a ^{2}} + \frac{3 b x f ^{2} - 3 b f ^{2} d + 3 b x c ^{2} - 3 b d c ^{2} + 6 b c x f - 6 b d c f}{a} - f^{3} - 3 f^{2} c - 3 f c^{2} - c^{3}

Solution steps

(\frac{b}{a} (x - d) - f - c)^{3}

Simplify

(\frac{b}{a} (x - d) - f - c)^{3} : (\frac{b}{a} (x - d) - f - c) (\frac{b}{a} (x - d) - f - c) (\frac{b}{a} (x - d) - f - c)

= (\frac{b}{a} (x - d) - f - c) (\frac{b}{a} (x - d) - f - c) (\frac{b}{a} (x - d) - f - c)

Expand

(\frac{b}{a} (x - d) - f - c) (\frac{b}{a} (x - d) - f - c) : \frac{b ^{2} ( x - d ) ( x - d )}{a ^{2}} + \frac{- 2 b x f + 2 b df - 2 b c x + 2 b d c}{a} + f^{2} + 2 c f + c^{2}

= (\frac{b ^{2} ( x - d ) ( x - d )}{a ^{2}} + \frac{- 2 b x f + 2 b df - 2 b c x + 2 b d c}{a} + f^{2} + 2 c f + c^{2}) (\frac{b}{a} (x - d) - f - c)

Distribute parentheses

= \frac{b ^{2} ( x - d ) ( x - d )}{a ^{2}} \cdot \frac{b}{a} (x - d) + \frac{b ^{2} ( x - d ) ( x - d )}{a ^{2}} (- f) + \frac{b ^{2} ( x - d ) ( x - d )}{a ^{2}} (- c) + \frac{- 2 b x f + 2 b df - 2 b c x + 2 b d c}{a} \cdot \frac{b}{a} (x - d) + \frac{- 2 b x f + 2 b df - 2 b c x + 2 b d c}{a} (- f) + \frac{- 2 b x f + 2 b df - 2 b c x + 2 b d c}{a} (- c) + f^{2} \frac{b}{a} (x - d) + f^{2} (- f) + f^{2} (- c) + 2 c f \frac{b}{a} (x - d) + 2 c f (- f) + 2 c f (- c) + c^{2} \frac{b}{a} (x - d) + c^{2} (- f) + c^{2} (- c)

Simplify

\frac{b ^{2} ( x - d ) ( x - d )}{a ^{2}} \cdot \frac{b}{a} (x - d) + \frac{b ^{2} ( x - d ) ( x - d )}{a ^{2}} (- f) + \frac{b ^{2} ( x - d ) ( x - d )}{a ^{2}} (- c) + \frac{- 2 b x f + 2 b df - 2 b c x + 2 b d c}{a} \cdot \frac{b}{a} (x - d) + \frac{- 2 b x f + 2 b df - 2 b c x + 2 b d c}{a} (- f) + \frac{- 2 b x f + 2 b df - 2 b c x + 2 b d c}{a} (- c) + f^{2} \frac{b}{a} (x - d) + f^{2} (- f) + f^{2} (- c) + 2 c f \frac{b}{a} (x - d) + 2 c f (- f) + 2 c f (- c) + c^{2} \frac{b}{a} (x - d) + c^{2} (- f) + c^{2} (- c) : \frac{b ^{3} ( x - d ) ( x - d ) ( x - d )}{a ^{3}} + \frac{- 3 b ^{2} x ^{2} f - 3 b ^{2} f d ^{2} - 3 b ^{2} x ^{2} c - 3 b ^{2} d ^{2} c + 2 b ^{2} d x f + 4 b ^{2} d c x + 2 d x b ^{2} f + 2 d c x b ^{2} + 2 x b ^{2} df}{a ^{2}} + \frac{3 b x f ^{2} - 3 b f ^{2} d + 3 b x c ^{2} - 3 b d c ^{2} + 6 b c x f - 6 b d c f}{a} - f^{3} - 3 f^{2} c - 3 f c^{2} - c^{3}

= \frac{b ^{3} ( x - d ) ( x - d ) ( x - d )}{a ^{3}} + \frac{- 3 b ^{2} x ^{2} f - 3 b ^{2} f d ^{2} - 3 b ^{2} x ^{2} c - 3 b ^{2} d ^{2} c + 2 b ^{2} d x f + 4 b ^{2} d c x + 2 d x b ^{2} f + 2 d c x b ^{2} + 2 x b ^{2} df}{a ^{2}} + \frac{3 b x f ^{2} - 3 b f ^{2} d + 3 b x c ^{2} - 3 b d c ^{2} + 6 b c x f - 6 b d c f}{a} - f^{3} - 3 f^{2} c - 3 f c^{2} - c^{3}

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