Question

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

Answer 1

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

Answer 2

Just distribute.  a^2 x a is a^3.  2a x a is 2a^2.  1 x a is a.  So far we have a^3 +2a^2+a.  Now do the other side.  a^2 x 1 is a^2.  2a x 1 is 2a. And 1 x 1 is 1.  Now we combine like terms. 2a^2 + a^2 is 3a^2. 2a + a is 3a. Now we just write the equation. a^3+3a^2+3a+1 is the answer.