Question

Using suitable identify, evaluate
a) ${\left(107\right)}^2$
b) $9\frac{1}{2}\times 10\frac{1}{2}$
c) ${\left(1.9\right)}^2$

Answer 1

a) $(107{)}^2=(100+7{)}^2$

$\Rightarrow (100{)}^2+(7{)}^2+2\left(100\right)\left(7\right)$

$\Rightarrow 11449$

$b)9\frac{1}{2}\times 10\frac{1}{2}=(10\frac{-1}{2}\left)\right(10+\frac{1}{2})$

$\Rightarrow (10{)}^2+-(\frac{1}{2}{)}^2=100-\frac{1}{4}=99\frac{3}{4}$

$c\left)\right(1.9{)}^2=(2-0.1{)}^2$

$=(2{)}^2+(0.1{)}^2-2\left(2\right)\left(0.1\right)$

=3.61