Find the Product (12x^2+7y^3)(4x^2+7y^3)

$(12 x^{2} + 7 y^{3}) (4 x^{2} + 7 y^{3})$

Expand $(12 x^{2} + 7 y^{3}) (4 x^{2} + 7 y^{3})$ using the FOIL Method.

Apply the distributive property.

$12 x^{2} (4 x^{2} + 7 y^{3}) + 7 y^{3} (4 x^{2} + 7 y^{3})$

Apply the distributive property.

$12 x^{2} (4 x^{2}) + 12 x^{2} (7 y^{3}) + 7 y^{3} (4 x^{2} + 7 y^{3})$

Apply the distributive property.

$12 x^{2} (4 x^{2}) + 12 x^{2} (7 y^{3}) + 7 y^{3} (4 x^{2}) + 7 y^{3} (7 y^{3})$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$12 \cdot 4 x^{2} x^{2} + 12 x^{2} (7 y^{3}) + 7 y^{3} (4 x^{2}) + 7 y^{3} (7 y^{3})$

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

Move $x^{2}$ .

$12 \cdot 4 (x^{2} x^{2}) + 12 x^{2} (7 y^{3}) + 7 y^{3} (4 x^{2}) + 7 y^{3} (7 y^{3})$

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

$12 \cdot 4 x^{2 + 2} + 12 x^{2} (7 y^{3}) + 7 y^{3} (4 x^{2}) + 7 y^{3} (7 y^{3})$

Add $2$ and $2$ .

$12 \cdot 4 x^{4} + 12 x^{2} (7 y^{3}) + 7 y^{3} (4 x^{2}) + 7 y^{3} (7 y^{3})$

Multiply $12$ by $4$ .

$48 x^{4} + 12 x^{2} (7 y^{3}) + 7 y^{3} (4 x^{2}) + 7 y^{3} (7 y^{3})$

Rewrite using the commutative property of multiplication.

$48 x^{4} + 12 \cdot 7 x^{2} y^{3} + 7 y^{3} (4 x^{2}) + 7 y^{3} (7 y^{3})$

Multiply $12$ by $7$ .

$48 x^{4} + 84 x^{2} y^{3} + 7 y^{3} (4 x^{2}) + 7 y^{3} (7 y^{3})$

Rewrite using the commutative property of multiplication.

$48 x^{4} + 84 x^{2} y^{3} + 7 \cdot 4 y^{3} x^{2} + 7 y^{3} (7 y^{3})$

Multiply $7$ by $4$ .

$48 x^{4} + 84 x^{2} y^{3} + 28 y^{3} x^{2} + 7 y^{3} (7 y^{3})$

Rewrite using the commutative property of multiplication.

$48 x^{4} + 84 x^{2} y^{3} + 28 y^{3} x^{2} + 7 \cdot 7 y^{3} y^{3}$

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

Move $y^{3}$ .

$48 x^{4} + 84 x^{2} y^{3} + 28 y^{3} x^{2} + 7 \cdot 7 (y^{3} y^{3})$

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

$48 x^{4} + 84 x^{2} y^{3} + 28 y^{3} x^{2} + 7 \cdot 7 y^{3 + 3}$

Add $3$ and $3$ .

$48 x^{4} + 84 x^{2} y^{3} + 28 y^{3} x^{2} + 7 \cdot 7 y^{6}$

Multiply $7$ by $7$ .

$48 x^{4} + 84 x^{2} y^{3} + 28 y^{3} x^{2} + 49 y^{6}$

Add $84 x^{2} y^{3}$ and $28 y^{3} x^{2}$ .

Move $y^{3}$ .

$48 x^{4} + 84 x^{2} y^{3} + 28 x^{2} y^{3} + 49 y^{6}$

Add $84 x^{2} y^{3}$ and $28 x^{2} y^{3}$ .

$48 x^{4} + 112 x^{2} y^{3} + 49 y^{6}$