Question

Find the product. (a2 + 2a + 1)(a + 1) a2 + 3a + 2 a3 + 3a2 + 3a + 1 a3 + 2a2 + a + 1 a3 + 3a2 + a + 1

Answer 1

(a2 + 2a + 1)(a + 1)

= a^3 + 2a^2 + a + a^2 + 2a + 1

= a^3 + 3a^2 + 3a + 1

Answer 2

`\text{The product is }a^3+3a^2+3a+1`

Explanation:

`\text{Given the expression }(a^2 + 2a + 1)(a + 1)`

we have to find the product.

`(a^2 + 2a + 1)(a + 1)`

Opening the brackets

`a^2(a+1)+2a(a+1)+1(a+1)`

Using distributive property, a.(b+c)=a.b+a.c

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

Combining like terms

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

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

which is required polynomial.

Option 2 is correct.