Find the Product (x^4+3y^3)(x^4-5y^3)

$(x^{4} + 3 y^{3}) (x^{4} - 5 y^{3})$

Expand $(x^{4} + 3 y^{3}) (x^{4} - 5 y^{3})$ using the FOIL Method.

Apply the distributive property.

$x^{4} (x^{4} - 5 y^{3}) + 3 y^{3} (x^{4} - 5 y^{3})$

Apply the distributive property.

$x^{4} x^{4} + x^{4} (- 5 y^{3}) + 3 y^{3} (x^{4} - 5 y^{3})$

Apply the distributive property.

$x^{4} x^{4} + x^{4} (- 5 y^{3}) + 3 y^{3} x^{4} + 3 y^{3} (- 5 y^{3})$

Simplify and combine like terms.

Simplify each term.

Multiply $x^{4}$ by $x^{4}$ by adding the exponents.

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

$x^{4 + 4} + x^{4} (- 5 y^{3}) + 3 y^{3} x^{4} + 3 y^{3} (- 5 y^{3})$

Add $4$ and $4$ .

$x^{8} + x^{4} (- 5 y^{3}) + 3 y^{3} x^{4} + 3 y^{3} (- 5 y^{3})$

Rewrite using the commutative property of multiplication.

$x^{8} - 5 x^{4} y^{3} + 3 y^{3} x^{4} + 3 y^{3} (- 5 y^{3})$

Rewrite using the commutative property of multiplication.

$x^{8} - 5 x^{4} y^{3} + 3 y^{3} x^{4} + 3 \cdot - 5 y^{3} y^{3}$

Multiply $y^{3}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$x^{8} - 5 x^{4} y^{3} + 3 y^{3} x^{4} + 3 \cdot - 5 (y^{3} y^{3})$

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

$x^{8} - 5 x^{4} y^{3} + 3 y^{3} x^{4} + 3 \cdot - 5 y^{3 + 3}$

Add $3$ and $3$ .

$x^{8} - 5 x^{4} y^{3} + 3 y^{3} x^{4} + 3 \cdot - 5 y^{6}$

Multiply $3$ by $- 5$ .

$x^{8} - 5 x^{4} y^{3} + 3 y^{3} x^{4} - 15 y^{6}$

Add $- 5 x^{4} y^{3}$ and $3 y^{3} x^{4}$ .

Move $y^{3}$ .

$x^{8} - 5 x^{4} y^{3} + 3 x^{4} y^{3} - 15 y^{6}$

Add $- 5 x^{4} y^{3}$ and $3 x^{4} y^{3}$ .

$x^{8} - 2 x^{4} y^{3} - 15 y^{6}$