Expand the Trigonometric Expression (-4c+1)(4c+1)

$(- 4 c + 1) (4 c + 1)$

Step 1

Expand $(- 4 c + 1) (4 c + 1)$ using the FOIL Method.

Apply the distributive property.

$- 4 c (4 c + 1) + 1 (4 c + 1)$

Apply the distributive property.

$- 4 c (4 c) - 4 c \cdot 1 + 1 (4 c + 1)$

Apply the distributive property.

$- 4 c (4 c) - 4 c \cdot 1 + 1 (4 c) + 1 \cdot 1$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 4 \cdot 4 c \cdot c - 4 c \cdot 1 + 1 (4 c) + 1 \cdot 1$

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

Move $c$ .

$- 4 \cdot 4 (c \cdot c) - 4 c \cdot 1 + 1 (4 c) + 1 \cdot 1$

Multiply $c$ by $c$ .

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

Multiply $- 4$ by $4$ .

$- 16 c^{2} - 4 c \cdot 1 + 1 (4 c) + 1 \cdot 1$

Multiply $- 4$ by $1$ .

$- 16 c^{2} - 4 c + 1 (4 c) + 1 \cdot 1$

Multiply $4 c$ by $1$ .

$- 16 c^{2} - 4 c + 4 c + 1 \cdot 1$

Multiply $1$ by $1$ .

$- 16 c^{2} - 4 c + 4 c + 1$

Add $- 4 c$ and $4 c$ .

$- 16 c^{2} + 0 + 1$

Add $- 16 c^{2}$ and $0$ .

$- 16 c^{2} + 1$