Simplify (-4a+b)(4a+b)

$(- 4 a + b) (4 a + b)$

Step 1

Expand $(- 4 a + b) (4 a + b)$ using the FOIL Method.

Apply the distributive property.

$- 4 a (4 a + b) + b (4 a + b)$

Apply the distributive property.

$- 4 a (4 a) - 4 a b + b (4 a + b)$

Apply the distributive property.

$- 4 a (4 a) - 4 a b + b (4 a) + b \cdot b$

Step 2

Simplify terms.

Combine the opposite terms in $- 4 a (4 a) - 4 a b + b (4 a) + b \cdot b$ .

Reorder the factors in the terms $- 4 a b$ and $b (4 a)$ .

$- 4 a (4 a) - 4 a b + 4 a b + b \cdot b$

Add $- 4 a b$ and $4 a b$ .

$- 4 a (4 a) + 0 + b \cdot b$

Add $- 4 a (4 a)$ and $0$ .

$- 4 a (4 a) + b \cdot b$

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 4 \cdot 4 a \cdot a + b \cdot b$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$- 4 \cdot 4 (a \cdot a) + b \cdot b$

Multiply $a$ by $a$ .

$- 4 \cdot 4 a^{2} + b \cdot b$

Multiply $- 4$ by $4$ .

$- 16 a^{2} + b \cdot b$

Multiply $b$ by $b$ .

$- 16 a^{2} + b^{2}$