Simplify (4g-1)(4g^2-5g-3)

$(4 g - 1) (4 g^{2} - 5 g - 3)$

Step 1

Expand $(4 g - 1) (4 g^{2} - 5 g - 3)$ by multiplying each term in the first expression by each term in the second expression.

$4 g (4 g^{2}) + 4 g (- 5 g) + 4 g \cdot - 3 - 1 (4 g^{2}) - 1 (- 5 g) - 1 \cdot - 3$

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 g \cdot g^{2} + 4 g (- 5 g) + 4 g \cdot - 3 - 1 (4 g^{2}) - 1 (- 5 g) - 1 \cdot - 3$

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

Move $g^{2}$ .

$4 \cdot 4 (g^{2} g) + 4 g (- 5 g) + 4 g \cdot - 3 - 1 (4 g^{2}) - 1 (- 5 g) - 1 \cdot - 3$

Multiply $g^{2}$ by $g$ .

Raise $g$ to the power of $1$ .

$4 \cdot 4 (g^{2} g^{1}) + 4 g (- 5 g) + 4 g \cdot - 3 - 1 (4 g^{2}) - 1 (- 5 g) - 1 \cdot - 3$

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

$4 \cdot 4 g^{2 + 1} + 4 g (- 5 g) + 4 g \cdot - 3 - 1 (4 g^{2}) - 1 (- 5 g) - 1 \cdot - 3$

Add $2$ and $1$ .

$4 \cdot 4 g^{3} + 4 g (- 5 g) + 4 g \cdot - 3 - 1 (4 g^{2}) - 1 (- 5 g) - 1 \cdot - 3$

Multiply $4$ by $4$ .

$16 g^{3} + 4 g (- 5 g) + 4 g \cdot - 3 - 1 (4 g^{2}) - 1 (- 5 g) - 1 \cdot - 3$

Rewrite using the commutative property of multiplication.

$16 g^{3} + 4 \cdot - 5 g \cdot g + 4 g \cdot - 3 - 1 (4 g^{2}) - 1 (- 5 g) - 1 \cdot - 3$

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

Move $g$ .

$16 g^{3} + 4 \cdot - 5 (g \cdot g) + 4 g \cdot - 3 - 1 (4 g^{2}) - 1 (- 5 g) - 1 \cdot - 3$

Multiply $g$ by $g$ .

$16 g^{3} + 4 \cdot - 5 g^{2} + 4 g \cdot - 3 - 1 (4 g^{2}) - 1 (- 5 g) - 1 \cdot - 3$

Multiply $4$ by $- 5$ .

$16 g^{3} - 20 g^{2} + 4 g \cdot - 3 - 1 (4 g^{2}) - 1 (- 5 g) - 1 \cdot - 3$

Multiply $- 3$ by $4$ .

$16 g^{3} - 20 g^{2} - 12 g - 1 (4 g^{2}) - 1 (- 5 g) - 1 \cdot - 3$

Multiply $4$ by $- 1$ .

$16 g^{3} - 20 g^{2} - 12 g - 4 g^{2} - 1 (- 5 g) - 1 \cdot - 3$

Multiply $- 5$ by $- 1$ .

$16 g^{3} - 20 g^{2} - 12 g - 4 g^{2} + 5 g - 1 \cdot - 3$

Multiply $- 1$ by $- 3$ .

$16 g^{3} - 20 g^{2} - 12 g - 4 g^{2} + 5 g + 3$

Simplify by adding terms.

Subtract $4 g^{2}$ from $- 20 g^{2}$ .

$16 g^{3} - 24 g^{2} - 12 g + 5 g + 3$

Add $- 12 g$ and $5 g$ .

$16 g^{3} - 24 g^{2} - 7 g + 3$