What is expand ((a+b)^2-(a-b)^2)^2 ?

The solution to expand ((a+b)^2-(a-b)^2)^2 is 18a^2b^2-2b^2a^2

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expand ((a+b)^2-(a-b)^2)^2

expand

((a + b)^{2} - (a - b)^{2})^{2}

18 a^{2} b^{2} - 2 b^{2} a^{2}

Solution steps

((a + b)^{2} - (a - b)^{2})^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

((a + b)^{2} - (a - b)^{2})^{2} = ((a + b)^{2})^{2} - 2 (a + b)^{2} (a - b)^{2} + ((a - b)^{2})^{2}

= ((a + b)^{2})^{2} - 2 (a + b)^{2} (a - b)^{2} + ((a - b)^{2})^{2}

Simplify

((a + b)^{2})^{2} - 2 (a + b)^{2} (a - b)^{2} + ((a - b)^{2})^{2} : (a + b)^{4} - 2 (a + b)^{2} (a - b)^{2} + (a - b)^{4}

= (a + b)^{4} - 2 (a + b)^{2} (a - b)^{2} + (a - b)^{4}

Expand

(a + b)^{4} : a^{4} + 4 a^{3} b + 6 a^{2} b^{2} + 4 a b^{3} + b^{4}

= a^{4} + 4 a^{3} b + 6 a^{2} b^{2} + 4 a b^{3} + b^{4} - 2 (a + b)^{2} (a - b)^{2} + (a - b)^{4}

Expand

- 2 (a + b)^{2} (a - b)^{2} : - 2 a^{4} - 2 b^{4} + 6 a^{2} b^{2} - 2 b^{2} a^{2}

= a^{4} + 4 a^{3} b + 6 a^{2} b^{2} + 4 a b^{3} + b^{4} - 2 a^{4} - 2 b^{4} + 6 a^{2} b^{2} - 2 b^{2} a^{2} + (a - b)^{4}

Expand

(a - b)^{4} : a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}

= a^{4} + 4 a^{3} b + 6 a^{2} b^{2} + 4 a b^{3} + b^{4} - 2 a^{4} - 2 b^{4} + 6 a^{2} b^{2} - 2 b^{2} a^{2} + a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}

Simplify

a^{4} + 4 a^{3} b + 6 a^{2} b^{2} + 4 a b^{3} + b^{4} - 2 a^{4} - 2 b^{4} + 6 a^{2} b^{2} - 2 b^{2} a^{2} + a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4} : 18 a^{2} b^{2} - 2 b^{2} a^{2}

= 18 a^{2} b^{2} - 2 b^{2} a^{2}

(3 x^{2} - 4 x - 5) (- 2 x^{2} + 2 x + 2)

\frac{50}{100}

j \cdot j

5 (2 x - 1)

What is expand ((a+b)^2-(a-b)^2)^2 ?
The solution to expand ((a+b)^2-(a-b)^2)^2 is 18a^2b^2-2b^2a^2