Question

Find the product. (a2 + 2a + 1)(a + 1)

Answer 1

Answer:

$a^3+3a^2+3a+1$

Explanation:

The given expression is

$(a^2+2a+1)(a+1)$

We need to find the product of $(a^2+2a+1)(a+1)$.

Using distributive property we get

$a^2(a+1)+2a(a+1)+1(a+1)$              $[\because a(b+c)=ab+ac]$

$a^2(a)+a^2(1)+2a(a)+2a(1)+a+1$

$a^3+a^2+2a^2+2a+a+1$

Combining like terms we get

$a^3+(a^2+2a^2)+(2a+a)+1$

$a^3+3a^2+3a+1$

Therefore, the product of $(a^2+2a+1)(a+1)$ is $a^3+3a^2+3a+1$.

Answer 2

$( a^{2} +2a+1) (a+1) \\ = ( a^{3} + a^{2} + 2a^{2} +2a+a+1) \\ = a^{3}+3 a^{2}+3a+1$