Simplify (y^2-3y)(y^2+3y)

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

Step 1

Expand $(y^{2} - 3 y) (y^{2} + 3 y)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

Combine the opposite terms in $y^{2} y^{2} + y^{2} (3 y) - 3 y \cdot y^{2} - 3 y (3 y)$ .

Reorder the factors in the terms $y^{2} (3 y)$ and $- 3 y \cdot y^{2}$ .

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

Subtract $3 y^{2} y$ from $3 y^{2} y$ .

$y^{2} y^{2} + 0 - 3 y (3 y)$

Add $y^{2} y^{2}$ and $0$ .

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

Simplify each term.

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

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

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

Add $2$ and $2$ .

$y^{4} - 3 y (3 y)$

Rewrite using the commutative property of multiplication.

$y^{4} - 3 \cdot 3 y \cdot y$

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

Move $y$ .

$y^{4} - 3 \cdot 3 (y \cdot y)$

Multiply $y$ by $y$ .

$y^{4} - 3 \cdot 3 y^{2}$

Multiply $- 3$ by $3$ .

$y^{4} - 9 y^{2}$