Question

Find the values using the suitable expansion formula:

$i).{105}^{2}ii).{94}^{2}iii).{32}^2-{28}^2$

Answer 1

i). By simplifying ${105}^2$, we get, $(100+5{)}^2$

So, we can use the formula; ${(x+y)}^2=x^2+2xy+y^2$

putting the values in the formula we get,
$(100+5{)}^2={100}^2+2\times 100\times 5+5^2=10000+1000+25=11025$

ii). By simplifying ${94}^2$, we get, $(100-6{)}^2$

So, we can use the formula; ${(x-y)}^2=x^2-2xy+y^2$

putting the values in the formula we get,
$(100-6{)}^2={100}^2-2\times 100\times 6+6^2=10000-1200+36=8836$
iii). We can use the formula; $x^2-y^2=(x+y)(x-y)$

putting the values in the formula we get,
${32}^2-{28}^2=(32+28)(32-28)=60\times 4=240$