Question

Simplify $a(a^2+a+1)+5$and find its value for$a=0,a=1anda=-1$.

Answer 1

Simplying expression:

The given expression is $a(a^2+a+1)+5$.

$a(a^2+a+1)+5=a\times a^2+a\times a+a\times 1+5$

$=a^3+a^2+a+5$

$\text{(i) For}a=0,a^3+a^2+a+5=(0{)}^3+(0{)}^2+\left(a\right)+5$

$=0+0+0+5=5$

$\text{(ii) For}a=1,a^3+a^2+a+5=(1{)}^3+(1{)}^2+\left(1\right)+5$

$=1+1+1+5=8$

$\text{(iii) For}a=-1,a^3+a^2+a+5=(-1{)}^3+(-1{)}^2+\left(1\right)+5$

$=-1+1-1+5=4$

Hence, correcr answers are $5,8and4$