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 \(a^3+3a^2+3a+1\).
