What is expand [(3ab+5cd)^2][(4ef-6gh)^2] ?

The solution to expand [(3ab+5cd)^2][(4ef-6gh)^2] is

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expand [(3ab+5cd)^2][(4ef-6gh)^2]

expand

[(3 ab + 5 c d)^{2}] [(4 e f - 6 g h)^{2}]

144 e^{2} a^{2} b^{2} f^{2} - 432 e a^{2} b^{2} f g h + 324 a^{2} b^{2} g^{2} h^{2} + 480 e^{2} ab c d f^{2} - 1440 e ab c df g h + 1080 ab c d g^{2} h^{2} + 400 e^{2} c^{2} d^{2} f^{2} - 1200 e c^{2} d^{2} f g h + 900 c^{2} d^{2} g^{2} h^{2}

Solution steps

((3 ab + 5 c d)^{2}) ((4 e f - 6 g h)^{2})

Remove parentheses:

(a) = a

= (3 ab + 5 c d)^{2} (4 e f - 6 g h)^{2}

(3 ab + 5 c d)^{2} = 9 a^{2} b^{2} + 30 ab c d + 25 c^{2} d^{2}

= (9 a^{2} b^{2} + 30 ab c d + 25 c^{2} d^{2}) (4 e f - 6 g h)^{2}

(4 e f - 6 g h)^{2} = 16 e^{2} f^{2} - 48 e f g h + 36 g^{2} h^{2}

= (9 a^{2} b^{2} + 30 ab c d + 25 c^{2} d^{2}) (16 e^{2} f^{2} - 48 e f g h + 36 g^{2} h^{2})

Distribute parentheses

= 9 a^{2} b^{2} \cdot 16 e^{2} f^{2} + 9 a^{2} b^{2} (- 48 e f g h) + 9 a^{2} b^{2} \cdot 36 g^{2} h^{2} + 30 ab c d \cdot 16 e^{2} f^{2} + 30 ab c d (- 48 e f g h) + 30 ab c d \cdot 36 g^{2} h^{2} + 25 c^{2} d^{2} \cdot 16 e^{2} f^{2} + 25 c^{2} d^{2} (- 48 e f g h) + 25 c^{2} d^{2} \cdot 36 g^{2} h^{2}

Apply minus-plus rules

+ (- a) = - a

= 9 \cdot 16 e^{2} a^{2} b^{2} f^{2} - 9 \cdot 48 e a^{2} b^{2} f g h + 9 \cdot 36 a^{2} b^{2} g^{2} h^{2} + 30 \cdot 16 e^{2} ab c d f^{2} - 30 \cdot 48 e ab c df g h + 30 \cdot 36 ab c d g^{2} h^{2} + 25 \cdot 16 e^{2} c^{2} d^{2} f^{2} - 25 \cdot 48 e c^{2} d^{2} f g h + 25 \cdot 36 c^{2} d^{2} g^{2} h^{2}

Simplify

9 \cdot 16 e^{2} a^{2} b^{2} f^{2} - 9 \cdot 48 e a^{2} b^{2} f g h + 9 \cdot 36 a^{2} b^{2} g^{2} h^{2} + 30 \cdot 16 e^{2} ab c d f^{2} - 30 \cdot 48 e ab c df g h + 30 \cdot 36 ab c d g^{2} h^{2} + 25 \cdot 16 e^{2} c^{2} d^{2} f^{2} - 25 \cdot 48 e c^{2} d^{2} f g h + 25 \cdot 36 c^{2} d^{2} g^{2} h^{2} : 144 e^{2} a^{2} b^{2} f^{2} - 432 e a^{2} b^{2} f g h + 324 a^{2} b^{2} g^{2} h^{2} + 480 e^{2} ab c d f^{2} - 1440 e ab c df g h + 1080 ab c d g^{2} h^{2} + 400 e^{2} c^{2} d^{2} f^{2} - 1200 e c^{2} d^{2} f g h + 900 c^{2} d^{2} g^{2} h^{2}

= 144 e^{2} a^{2} b^{2} f^{2} - 432 e a^{2} b^{2} f g h + 324 a^{2} b^{2} g^{2} h^{2} + 480 e^{2} ab c d f^{2} - 1440 e ab c df g h + 1080 ab c d g^{2} h^{2} + 400 e^{2} c^{2} d^{2} f^{2} - 1200 e c^{2} d^{2} f g h + 900 c^{2} d^{2} g^{2} h^{2}

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

(u + \frac{1}{x}) d x

(x - 2)^{2}

x + 9^{2}

\frac{x}{( s + 1 ) ^{2}}

What is expand [(3ab+5cd)^2][(4ef-6gh)^2] ?
The solution to expand [(3ab+5cd)^2][(4ef-6gh)^2] is