Expand the Trigonometric Expression (y^2-9)(y^2-4)

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

Step 1

Expand $(y^{2} - 9) (y^{2} - 4)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

$y^{2} y^{2} + y^{2} \cdot - 4 - 9 (y^{2} - 4)$

Apply the distributive property.

$y^{2} y^{2} + y^{2} \cdot - 4 - 9 y^{2} - 9 \cdot - 4$

Step 2

Simplify and combine like terms.

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.

$y^{2 + 2} + y^{2} \cdot - 4 - 9 y^{2} - 9 \cdot - 4$

Add $2$ and $2$ .

$y^{4} + y^{2} \cdot - 4 - 9 y^{2} - 9 \cdot - 4$

Move $- 4$ to the left of $y^{2}$ .

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

Multiply $- 9$ by $- 4$ .

$y^{4} - 4 y^{2} - 9 y^{2} + 36$

Subtract $9 y^{2}$ from $- 4 y^{2}$ .

$y^{4} - 13 y^{2} + 36$