Write in Standard Form (g+6)(6g^2+9g-8)

$(g + 6) (6 g^{2} + 9 g - 8)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Expand $(g + 6) (6 g^{2} + 9 g - 8)$ by multiplying each term in the first expression by each term in the second expression.

$g (6 g^{2}) + g (9 g) + g \cdot - 8 + 6 (6 g^{2}) + 6 (9 g) + 6 \cdot - 8$

Step 3

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$6 g \cdot g^{2} + g (9 g) + g \cdot - 8 + 6 (6 g^{2}) + 6 (9 g) + 6 \cdot - 8$

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

Move $g^{2}$ .

$6 (g^{2} g) + g (9 g) + g \cdot - 8 + 6 (6 g^{2}) + 6 (9 g) + 6 \cdot - 8$

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

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

$6 (g^{2} g^{1}) + g (9 g) + g \cdot - 8 + 6 (6 g^{2}) + 6 (9 g) + 6 \cdot - 8$

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

$6 g^{2 + 1} + g (9 g) + g \cdot - 8 + 6 (6 g^{2}) + 6 (9 g) + 6 \cdot - 8$

Add $2$ and $1$ .

$6 g^{3} + g (9 g) + g \cdot - 8 + 6 (6 g^{2}) + 6 (9 g) + 6 \cdot - 8$

Rewrite using the commutative property of multiplication.

$6 g^{3} + 9 g \cdot g + g \cdot - 8 + 6 (6 g^{2}) + 6 (9 g) + 6 \cdot - 8$

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

Move $g$ .

$6 g^{3} + 9 (g \cdot g) + g \cdot - 8 + 6 (6 g^{2}) + 6 (9 g) + 6 \cdot - 8$

Multiply $g$ by $g$ .

$6 g^{3} + 9 g^{2} + g \cdot - 8 + 6 (6 g^{2}) + 6 (9 g) + 6 \cdot - 8$

Move $- 8$ to the left of $g$ .

$6 g^{3} + 9 g^{2} - 8 \cdot g + 6 (6 g^{2}) + 6 (9 g) + 6 \cdot - 8$

Multiply $6$ by $6$ .

$6 g^{3} + 9 g^{2} - 8 g + 36 g^{2} + 6 (9 g) + 6 \cdot - 8$

Multiply $9$ by $6$ .

$6 g^{3} + 9 g^{2} - 8 g + 36 g^{2} + 54 g + 6 \cdot - 8$

Multiply $6$ by $- 8$ .

$6 g^{3} + 9 g^{2} - 8 g + 36 g^{2} + 54 g - 48$

Simplify by adding terms.

Add $9 g^{2}$ and $36 g^{2}$ .

$6 g^{3} + 45 g^{2} - 8 g + 54 g - 48$

Add $- 8 g$ and $54 g$ .

$6 g^{3} + 45 g^{2} + 46 g - 48$