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

The solution to (a^2+b)^2-(a^2-b)^2 is 4a^2b

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

simplify

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

4 a^{2} b

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

a^{4} - a^{4} = 0

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

Add similar elements:

2 a^{2} b + 2 a^{2} b = 4 a^{2} b

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

Add similar elements:

b^{2} - b^{2} = 0

= 4 a^{2} b

4 x^{2} + 8 x - 21

- 7 + (- 10)

- 11 + (- 3)

46 \cdot 3

a \cdot 0