What is |a+b|^2-|a-b|^2 ?

The solution to |a+b|^2-|a-b|^2 is 4ab

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simplify |a+b|^2-|a-b|^2

simplify

∣ a + b ∣^{2} - ∣ a - b ∣^{2}

4 ab

Solution steps

∣ a + b ∣^{2} - ∣ a - b ∣^{2}

∣ a + b ∣^{2} = (a + b)^{2}

∣ a - b ∣^{2} = (a - b)^{2}

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

a^{2} - a^{2} = 0

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

Add similar elements:

2 ab + 2 ab = 4 ab

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

Add similar elements:

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

= 4 ab

32 y^{5} - 1

(\frac{x y ^{- 1}}{2 x ^{2} y ^{- 2}})^{- 3}

v (t)

\frac{2}{5} \cdot \frac{15}{4}

\frac{2}{1} + \frac{1}{3}