Question

Using the identities of algebraic expressions, Find :

$\left(i\right){102}^2$

$\left(ii\right){53}^2$

$\left(iii\right){1001}^2$ [3 MARKS]

Answer 1

Application: 1 Mark each

Using the identity :
$(a+b{)}^2=a^2+2ab+b^2$

$\left(i\right)(102{)}^2$

$\Rightarrow (100+2{)}^2$

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

$\Rightarrow 10000+4+400$

$\Rightarrow 10404$


$\left(ii\right)(53{)}^2$

$\Rightarrow (50+3{)}^2$

$\Rightarrow (50{)}^2+(3{)}^2+2\left(50\right)\left(3\right)$

$\Rightarrow 2500+9+300$

$\Rightarrow 2809$


$\left(iii\right)(1001{)}^2$

$\Rightarrow (1000+1{)}^2$

$\Rightarrow (1000{)}^2+(1{)}^2+2\left(1000\right)\left(1\right)$

$\Rightarrow 1000000+1+2000$

$\Rightarrow 1002001$