Find the Product (y+3)(y^2-3y+9)

$(y + 3) (y^{2} - 3 y + 9)$

Step 1

Expand $(y + 3) (y^{2} - 3 y + 9)$ by multiplying each term in the first expression by each term in the second expression.

$y \cdot y^{2} + y (- 3 y) + y \cdot 9 + 3 y^{2} + 3 (- 3 y) + 3 \cdot 9$

Step 2

Simplify terms.

Simplify each term.

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

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

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

$y^{1} y^{2} + y (- 3 y) + y \cdot 9 + 3 y^{2} + 3 (- 3 y) + 3 \cdot 9$

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

$y^{1 + 2} + y (- 3 y) + y \cdot 9 + 3 y^{2} + 3 (- 3 y) + 3 \cdot 9$

Add $1$ and $2$ .

$y^{3} + y (- 3 y) + y \cdot 9 + 3 y^{2} + 3 (- 3 y) + 3 \cdot 9$

Rewrite using the commutative property of multiplication.

$y^{3} - 3 y \cdot y + y \cdot 9 + 3 y^{2} + 3 (- 3 y) + 3 \cdot 9$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$y^{3} - 3 (y \cdot y) + y \cdot 9 + 3 y^{2} + 3 (- 3 y) + 3 \cdot 9$

Multiply $y$ by $y$ .

$y^{3} - 3 y^{2} + y \cdot 9 + 3 y^{2} + 3 (- 3 y) + 3 \cdot 9$

Move $9$ to the left of $y$ .

$y^{3} - 3 y^{2} + 9 \cdot y + 3 y^{2} + 3 (- 3 y) + 3 \cdot 9$

Multiply $- 3$ by $3$ .

$y^{3} - 3 y^{2} + 9 y + 3 y^{2} - 9 y + 3 \cdot 9$

Multiply $3$ by $9$ .

$y^{3} - 3 y^{2} + 9 y + 3 y^{2} - 9 y + 27$

Combine the opposite terms in $y^{3} - 3 y^{2} + 9 y + 3 y^{2} - 9 y + 27$ .

Add $- 3 y^{2}$ and $3 y^{2}$ .

$y^{3} + 9 y + 0 - 9 y + 27$

Add $y^{3} + 9 y$ and $0$ .

$y^{3} + 9 y - 9 y + 27$

Subtract $9 y$ from $9 y$ .

$y^{3} + 0 + 27$

Add $y^{3}$ and $0$ .

$y^{3} + 27$