Expand the Trigonometric Expression (c^2-6)(2c^2+3c-1)

$(c^{2} - 6) (2 c^{2} + 3 c - 1)$

Step 1

Expand $(c^{2} - 6) (2 c^{2} + 3 c - 1)$ by multiplying each term in the first expression by each term in the second expression.

$c^{2} (2 c^{2}) + c^{2} (3 c) + c^{2} \cdot - 1 - 6 (2 c^{2}) - 6 (3 c) - 6 \cdot - 1$

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 c^{2} c^{2} + c^{2} (3 c) + c^{2} \cdot - 1 - 6 (2 c^{2}) - 6 (3 c) - 6 \cdot - 1$

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

Move $c^{2}$ .

$2 (c^{2} c^{2}) + c^{2} (3 c) + c^{2} \cdot - 1 - 6 (2 c^{2}) - 6 (3 c) - 6 \cdot - 1$

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

$2 c^{2 + 2} + c^{2} (3 c) + c^{2} \cdot - 1 - 6 (2 c^{2}) - 6 (3 c) - 6 \cdot - 1$

Add $2$ and $2$ .

$2 c^{4} + c^{2} (3 c) + c^{2} \cdot - 1 - 6 (2 c^{2}) - 6 (3 c) - 6 \cdot - 1$

Rewrite using the commutative property of multiplication.

$2 c^{4} + 3 c^{2} c + c^{2} \cdot - 1 - 6 (2 c^{2}) - 6 (3 c) - 6 \cdot - 1$

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

Move $c$ .

$2 c^{4} + 3 (c \cdot c^{2}) + c^{2} \cdot - 1 - 6 (2 c^{2}) - 6 (3 c) - 6 \cdot - 1$

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

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

$2 c^{4} + 3 (c^{1} c^{2}) + c^{2} \cdot - 1 - 6 (2 c^{2}) - 6 (3 c) - 6 \cdot - 1$

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

$2 c^{4} + 3 c^{1 + 2} + c^{2} \cdot - 1 - 6 (2 c^{2}) - 6 (3 c) - 6 \cdot - 1$

Add $1$ and $2$ .

$2 c^{4} + 3 c^{3} + c^{2} \cdot - 1 - 6 (2 c^{2}) - 6 (3 c) - 6 \cdot - 1$

Move $- 1$ to the left of $c^{2}$ .

$2 c^{4} + 3 c^{3} - 1 \cdot c^{2} - 6 (2 c^{2}) - 6 (3 c) - 6 \cdot - 1$

Rewrite $- 1 c^{2}$ as $- c^{2}$ .

$2 c^{4} + 3 c^{3} - c^{2} - 6 (2 c^{2}) - 6 (3 c) - 6 \cdot - 1$

Multiply $2$ by $- 6$ .

$2 c^{4} + 3 c^{3} - c^{2} - 12 c^{2} - 6 (3 c) - 6 \cdot - 1$

Multiply $3$ by $- 6$ .

$2 c^{4} + 3 c^{3} - c^{2} - 12 c^{2} - 18 c - 6 \cdot - 1$

Multiply $- 6$ by $- 1$ .

$2 c^{4} + 3 c^{3} - c^{2} - 12 c^{2} - 18 c + 6$

Subtract $12 c^{2}$ from $- c^{2}$ .

$2 c^{4} + 3 c^{3} - 13 c^{2} - 18 c + 6$