Simplify (a^2+2a+1)(a+1)

$(a^{2} + 2 a + 1) (a + 1)$

Step 1

Expand $(a^{2} + 2 a + 1) (a + 1)$ by multiplying each term in the first expression by each term in the second expression.

$a^{2} a + a^{2} \cdot 1 + 2 a \cdot a + 2 a \cdot 1 + 1 a + 1 \cdot 1$

Step 2

Simplify terms.

Simplify each term.

Multiply $a^{2}$ by $a$ by adding the exponents.

Multiply $a^{2}$ by $a$ .

Raise $a$ to the power of $1$ .

$a^{2} a^{1} + a^{2} \cdot 1 + 2 a \cdot a + 2 a \cdot 1 + 1 a + 1 \cdot 1$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a^{2 + 1} + a^{2} \cdot 1 + 2 a \cdot a + 2 a \cdot 1 + 1 a + 1 \cdot 1$

Add $2$ and $1$ .

$a^{3} + a^{2} \cdot 1 + 2 a \cdot a + 2 a \cdot 1 + 1 a + 1 \cdot 1$

Multiply $a^{2}$ by $1$ .

$a^{3} + a^{2} + 2 a \cdot a + 2 a \cdot 1 + 1 a + 1 \cdot 1$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$a^{3} + a^{2} + 2 (a \cdot a) + 2 a \cdot 1 + 1 a + 1 \cdot 1$

Multiply $a$ by $a$ .

$a^{3} + a^{2} + 2 a^{2} + 2 a \cdot 1 + 1 a + 1 \cdot 1$

Multiply $2$ by $1$ .

$a^{3} + a^{2} + 2 a^{2} + 2 a + 1 a + 1 \cdot 1$

Multiply $a$ by $1$ .

$a^{3} + a^{2} + 2 a^{2} + 2 a + a + 1 \cdot 1$

Multiply $1$ by $1$ .

$a^{3} + a^{2} + 2 a^{2} + 2 a + a + 1$

Simplify by adding terms.

Add $a^{2}$ and $2 a^{2}$ .

$a^{3} + 3 a^{2} + 2 a + a + 1$

Add $2 a$ and $a$ .

$a^{3} + 3 a^{2} + 3 a + 1$