How do you simplify ${(x + i)}^{2} - {(x - i)}^{2}$ $(x+i)^2-(x-i)^2$ ?

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Answer 1 · 2017-01-15T10:51:39

${(x + i)}^{2} - {(x - i)}^{2} = 4 i x$ $(x+i)^2-(x-i)^2 = 4ix$

Note that in general:

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

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

So:

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

In our example:

${(x + i)}^{2} - {(x - i)}^{2} = 4 i x$ $(x+i)^2-(x-i)^2 = 4ix$

How do you simplify (x+i)2−(x−i)2(x+i)^2-(x-i)^2?