Question

Simplify ${(1-z)}^2-{(1+z)}^2$

Answer 1

Given equation $(1-2{)}^2-(1+z{)}^2$

Since, we know that $(a-b{)}^2=a^2+b^2-2ab---(1)$

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

So, using formulas we get

$(1-z{)}^2=1^2+z^2-\mathrm{2.1.}z\left\{1\right\}---(3)$

$(1+z{)}^2=1^2+z^2+\mathrm{2.1.}z\left\{2\right\}---(4)$

Subtract $\left(4\right)$ from $\left(3\right)$

i.e. $(1-z{)}^2-(1+z{)}^2=1+z^2-2z-1-z^2-2z$

$=-4z$