Expand the Trigonometric Expression (c+8)(8c+2)

$(c + 8) (8 c + 2)$

Step 1

Expand $(c + 8) (8 c + 2)$ using the FOIL Method.

Apply the distributive property.

$c (8 c + 2) + 8 (8 c + 2)$

Apply the distributive property.

$c (8 c) + c \cdot 2 + 8 (8 c + 2)$

Apply the distributive property.

$c (8 c) + c \cdot 2 + 8 (8 c) + 8 \cdot 2$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$8 c \cdot c + c \cdot 2 + 8 (8 c) + 8 \cdot 2$

Multiply $c$ by $c$ by adding the exponents.

Move $c$ .

$8 (c \cdot c) + c \cdot 2 + 8 (8 c) + 8 \cdot 2$

Multiply $c$ by $c$ .

$8 c^{2} + c \cdot 2 + 8 (8 c) + 8 \cdot 2$

Move $2$ to the left of $c$ .

$8 c^{2} + 2 \cdot c + 8 (8 c) + 8 \cdot 2$

Multiply $8$ by $8$ .

$8 c^{2} + 2 c + 64 c + 8 \cdot 2$

Multiply $8$ by $2$ .

$8 c^{2} + 2 c + 64 c + 16$

Add $2 c$ and $64 c$ .

$8 c^{2} + 66 c + 16$