What is expand (bf-ec-af+cd+ea-bd)^2*(a^2+b^2+c^2) ?

The solution to expand (bf-ec-af+cd+ea-bd)^2*(a^2+b^2+c^2) is

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expand (bf-ec-af+cd+ea-bd)^2*(a^2+b^2+c^2)

expand

(b f - ec - a f + c d + e a - b d)^{2} \cdot (a^{2} + b^{2} + c^{2})

b^{4} f^{2} + b^{4} d^{2} - 2 b^{4} fd - 2 e b^{3} f c - 2 b^{3} f^{2} a + 2 e b^{3} f a - 2 b^{3} c d^{2} + 2 b^{3} f c d + 2 e b^{3} c d + 2 b^{3} f a d - 2 e b^{3} a d + e^{2} b^{2} c^{2} + b^{2} f^{2} c^{2} + 2 b^{2} f^{2} a^{2} - 2 e b^{2} f a^{2} + e^{2} b^{2} a^{2} + 2 e b^{2} f c a - 2 e^{2} b^{2} c a + b^{2} a^{2} d^{2} + 2 b^{2} c^{2} d^{2} - 2 b^{2} f a^{2} d - 2 e b^{2} c^{2} d - 2 b^{2} f c a d + 2 e b^{2} c a d - 2 b^{2} f c^{2} d - 2 e b f c^{3} - 2 b f^{2} a^{3} + 2 e b f a^{3} - 2 e b f c a^{2} - 2 b f^{2} c^{2} a + 2 e b f c^{2} a - 2 b c a^{2} d^{2} - 2 b c^{3} d^{2} + 2 b f c a^{2} d + 2 e b c a^{2} d + 2 b f a^{3} d - 2 e b a^{3} d + 2 b f c^{3} d + 2 e b c^{3} d + 2 b f c^{2} a d - 2 e b c^{2} a d + e^{2} c^{4} + f^{2} a^{4} - 2 e f a^{4} + e^{2} a^{4} + 2 e f c a^{3} - 2 e^{2} c a^{3} + 2 e^{2} c^{2} a^{2} + f^{2} c^{2} a^{2} - 2 e f c^{2} a^{2} + 2 e f c^{3} a - 2 e^{2} c^{3} a + c^{2} a^{2} d^{2} + c^{4} d^{2} - 2 e c^{2} a^{2} d - 2 f c a^{3} d + 2 ec a^{3} d - 2 e c^{4} d - 2 f c^{3} a d + 2 e c^{3} a d

Solution steps

(b f - ec - a f + c d + e a - b d)^{2} (a^{2} + b^{2} + c^{2})

= (b f - ec - f a + c d + e a - b d)^{2} (a^{2} + b^{2} + c^{2})

Distribute parentheses

= (b f - ec - a f + c d + e a - b d)^{2} a^{2} + (b f - ec - a f + c d + e a - b d)^{2} b^{2} + (b f - ec - a f + c d + e a - b d)^{2} c^{2}

= a^{2} (b f - ec - f a + c d + e a - b d)^{2} + b^{2} (b f - ec - f a + c d + e a - b d)^{2} + c^{2} (b f - ec - f a + c d + e a - b d)^{2}

Simplify

a^{2} (b f - ec - f a + c d + e a - b d)^{2} + b^{2} (b f - ec - f a + c d + e a - b d)^{2} + c^{2} (b f - ec - f a + c d + e a - b d)^{2} : b^{4} f^{2} + b^{4} d^{2} - 2 b^{4} fd - 2 e b^{3} f c - 2 b^{3} f^{2} a + 2 e b^{3} f a - 2 b^{3} c d^{2} + 2 b^{3} f c d + 2 e b^{3} c d + 2 b^{3} f a d - 2 e b^{3} a d + e^{2} b^{2} c^{2} + b^{2} f^{2} c^{2} + 2 b^{2} f^{2} a^{2} - 2 e b^{2} f a^{2} + e^{2} b^{2} a^{2} + 2 e b^{2} f c a - 2 e^{2} b^{2} c a + b^{2} a^{2} d^{2} + 2 b^{2} c^{2} d^{2} - 2 b^{2} f a^{2} d - 2 e b^{2} c^{2} d - 2 b^{2} f c a d + 2 e b^{2} c a d - 2 b^{2} f c^{2} d - 2 e b f c^{3} - 2 b f^{2} a^{3} + 2 e b f a^{3} - 2 e b f c a^{2} - 2 b f^{2} c^{2} a + 2 e b f c^{2} a - 2 b c a^{2} d^{2} - 2 b c^{3} d^{2} + 2 b f c a^{2} d + 2 e b c a^{2} d + 2 b f a^{3} d - 2 e b a^{3} d + 2 b f c^{3} d + 2 e b c^{3} d + 2 b f c^{2} a d - 2 e b c^{2} a d + e^{2} c^{4} + f^{2} a^{4} - 2 e f a^{4} + e^{2} a^{4} + 2 e f c a^{3} - 2 e^{2} c a^{3} + 2 e^{2} c^{2} a^{2} + f^{2} c^{2} a^{2} - 2 e f c^{2} a^{2} + 2 e f c^{3} a - 2 e^{2} c^{3} a + c^{2} a^{2} d^{2} + c^{4} d^{2} - 2 e c^{2} a^{2} d - 2 f c a^{3} d + 2 ec a^{3} d - 2 e c^{4} d - 2 f c^{3} a d + 2 e c^{3} a d

= b^{4} f^{2} + b^{4} d^{2} - 2 b^{4} fd - 2 e b^{3} f c - 2 b^{3} f^{2} a + 2 e b^{3} f a - 2 b^{3} c d^{2} + 2 b^{3} f c d + 2 e b^{3} c d + 2 b^{3} f a d - 2 e b^{3} a d + e^{2} b^{2} c^{2} + b^{2} f^{2} c^{2} + 2 b^{2} f^{2} a^{2} - 2 e b^{2} f a^{2} + e^{2} b^{2} a^{2} + 2 e b^{2} f c a - 2 e^{2} b^{2} c a + b^{2} a^{2} d^{2} + 2 b^{2} c^{2} d^{2} - 2 b^{2} f a^{2} d - 2 e b^{2} c^{2} d - 2 b^{2} f c a d + 2 e b^{2} c a d - 2 b^{2} f c^{2} d - 2 e b f c^{3} - 2 b f^{2} a^{3} + 2 e b f a^{3} - 2 e b f c a^{2} - 2 b f^{2} c^{2} a + 2 e b f c^{2} a - 2 b c a^{2} d^{2} - 2 b c^{3} d^{2} + 2 b f c a^{2} d + 2 e b c a^{2} d + 2 b f a^{3} d - 2 e b a^{3} d + 2 b f c^{3} d + 2 e b c^{3} d + 2 b f c^{2} a d - 2 e b c^{2} a d + e^{2} c^{4} + f^{2} a^{4} - 2 e f a^{4} + e^{2} a^{4} + 2 e f c a^{3} - 2 e^{2} c a^{3} + 2 e^{2} c^{2} a^{2} + f^{2} c^{2} a^{2} - 2 e f c^{2} a^{2} + 2 e f c^{3} a - 2 e^{2} c^{3} a + c^{2} a^{2} d^{2} + c^{4} d^{2} - 2 e c^{2} a^{2} d - 2 f c a^{3} d + 2 ec a^{3} d - 2 e c^{4} d - 2 f c^{3} a d + 2 e c^{3} a d

(x - \frac{3}{4}) (x - 2)

(c - 5) (c + 5)

f (x) = \frac{2 x}{( 6 - 3 x ^{2} ) ^{6}}

\frac{ln ( x )}{( x - 4 ) ^{3}}

tan (x) (1 - cot (x)) + 1

What is expand (bf-ec-af+cd+ea-bd)^2*(a^2+b^2+c^2) ?
The solution to expand (bf-ec-af+cd+ea-bd)^2*(a^2+b^2+c^2) is