Question

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

Answer 1

`( a^(2) +2a+1) (a+1) \\ = ( a^(3) + a^(2) + 2a^(2) +2a+a+1) \\ = a^(3)+3 a^(2)+3a+1`

Answer 2

`a^3+3a^2+3a+1`

Step-by-step 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`.