Answer:
[tex]a^3+3a^2+3a+1[/tex]
Explanation:
The given expression is
[tex](a^2+2a+1)(a+1)[/tex]
We need to find the product of [tex](a^2+2a+1)(a+1)[/tex].
Using distributive property we get
[tex]a^2(a+1)+2a(a+1)+1(a+1)[/tex] [tex][\because a(b+c)=ab+ac][/tex]
[tex]a^2(a)+a^2(1)+2a(a)+2a(1)+a+1[/tex]
[tex]a^3+a^2+2a^2+2a+a+1[/tex]
Combining like terms we get
[tex]a^3+(a^2+2a^2)+(2a+a)+1[/tex]
[tex]a^3+3a^2+3a+1[/tex]
Therefore, the product of [tex](a^2+2a+1)(a+1)[/tex] is [tex]a^3+3a^2+3a+1[/tex].
