Question

Calculate the value of the expression using suitable identity $({23}^2-{22}^2{)}^2$.

Answer 1

The given expression is

$({23}^2-{22}^2{)}^2$

$={\left[\right(23+22\left)\right(23-22\left)\right]}^2[a^2-b^2=(a+b\left)\right(a-b\left)\right]$

$=(45\times 1{)}^2$ [1 mark]

$=(40+5{)}^2$

$=(40{)}^2+(5{)}^2+2\left(40\right)\left(5\right)$

$=1600+25+400$

$=2025$ [1 mark]