Simplify (4g+3h)(2g+3h)

$(4 g + 3 h) (2 g + 3 h)$

Step 1

Expand $(4 g + 3 h) (2 g + 3 h)$ using the FOIL Method.

Apply the distributive property.

$4 g (2 g + 3 h) + 3 h (2 g + 3 h)$

Apply the distributive property.

$4 g (2 g) + 4 g (3 h) + 3 h (2 g + 3 h)$

Apply the distributive property.

$4 g (2 g) + 4 g (3 h) + 3 h (2 g) + 3 h (3 h)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 2 g \cdot g + 4 g (3 h) + 3 h (2 g) + 3 h (3 h)$

Multiply $g$ by $g$ by adding the exponents.

Move $g$ .

$4 \cdot 2 (g \cdot g) + 4 g (3 h) + 3 h (2 g) + 3 h (3 h)$

Multiply $g$ by $g$ .

$4 \cdot 2 g^{2} + 4 g (3 h) + 3 h (2 g) + 3 h (3 h)$

Multiply $4$ by $2$ .

$8 g^{2} + 4 g (3 h) + 3 h (2 g) + 3 h (3 h)$

Rewrite using the commutative property of multiplication.

$8 g^{2} + 4 \cdot 3 g h + 3 h (2 g) + 3 h (3 h)$

Multiply $4$ by $3$ .

$8 g^{2} + 12 g h + 3 h (2 g) + 3 h (3 h)$

Rewrite using the commutative property of multiplication.

$8 g^{2} + 12 g h + 3 \cdot 2 h g + 3 h (3 h)$

Multiply $3$ by $2$ .

$8 g^{2} + 12 g h + 6 h g + 3 h (3 h)$

Rewrite using the commutative property of multiplication.

$8 g^{2} + 12 g h + 6 h g + 3 \cdot 3 h \cdot h$

Multiply $h$ by $h$ by adding the exponents.

Move $h$ .

$8 g^{2} + 12 g h + 6 h g + 3 \cdot 3 (h \cdot h)$

Multiply $h$ by $h$ .

$8 g^{2} + 12 g h + 6 h g + 3 \cdot 3 h^{2}$

Multiply $3$ by $3$ .

$8 g^{2} + 12 g h + 6 h g + 9 h^{2}$

Add $12 g h$ and $6 h g$ .

Move $h$ .

$8 g^{2} + 12 g h + 6 g h + 9 h^{2}$

Add $12 g h$ and $6 g h$ .

$8 g^{2} + 18 g h + 9 h^{2}$