Question

Question 25
Using suitable identity, evaluate the following
(i) ${103}^3$

(ii) $101\times 102$

(iii) ${999}^2$

Answer 1

(i) ${103}^3=(100+3{)}^3$
$=(100{)}^3+(3{)}^3+3\times 100\times 3(100+3)$ [Using the identity, $(a+b{)}^3=a^3+b^3+3ab(a+b)$]
$=1000000+27+900\left(103\right)$
$=1000027+92700=1092727$

(ii) $101\times 102=(100+1)(100+2)$
$=(100{)}^2+100(1+2)+1\times 2$ [Using the identity, $(x+a)(x+b)=x^2+x(a+b)+ab$]
$=10000+300+2=10302$

(iii) $(999{)}^2=(1000-1{)}^2$
$=(1000{)}^2+(1{)}^2–2\times 1000\times 1$ [Using the identity, $(a–b{)}^2=a^2+b^2–2ab$]
$=1000000+1–2000=998001$