Find the Product (4a+5b)(4a-5b)

$(4 a + 5 b) (4 a - 5 b)$

Step 1

Expand $(4 a + 5 b) (4 a - 5 b)$ using the FOIL Method.

Apply the distributive property.

$4 a (4 a - 5 b) + 5 b (4 a - 5 b)$

Apply the distributive property.

$4 a (4 a) + 4 a (- 5 b) + 5 b (4 a - 5 b)$

Apply the distributive property.

$4 a (4 a) + 4 a (- 5 b) + 5 b (4 a) + 5 b (- 5 b)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 a \cdot a + 4 a (- 5 b) + 5 b (4 a) + 5 b (- 5 b)$

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

Move $a$ .

$4 \cdot 4 (a \cdot a) + 4 a (- 5 b) + 5 b (4 a) + 5 b (- 5 b)$

Multiply $a$ by $a$ .

$4 \cdot 4 a^{2} + 4 a (- 5 b) + 5 b (4 a) + 5 b (- 5 b)$

Multiply $4$ by $4$ .

$16 a^{2} + 4 a (- 5 b) + 5 b (4 a) + 5 b (- 5 b)$

Rewrite using the commutative property of multiplication.

$16 a^{2} + 4 \cdot - 5 a b + 5 b (4 a) + 5 b (- 5 b)$

Multiply $4$ by $- 5$ .

$16 a^{2} - 20 a b + 5 b (4 a) + 5 b (- 5 b)$

Rewrite using the commutative property of multiplication.

$16 a^{2} - 20 a b + 5 \cdot 4 b a + 5 b (- 5 b)$

Multiply $5$ by $4$ .

$16 a^{2} - 20 a b + 20 b a + 5 b (- 5 b)$

Rewrite using the commutative property of multiplication.

$16 a^{2} - 20 a b + 20 b a + 5 \cdot - 5 b \cdot b$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$16 a^{2} - 20 a b + 20 b a + 5 \cdot - 5 (b \cdot b)$

Multiply $b$ by $b$ .

$16 a^{2} - 20 a b + 20 b a + 5 \cdot - 5 b^{2}$

Multiply $5$ by $- 5$ .

$16 a^{2} - 20 a b + 20 b a - 25 b^{2}$

Add $- 20 a b$ and $20 b a$ .

Move $b$ .

$16 a^{2} - 20 a b + 20 a b - 25 b^{2}$

Add $- 20 a b$ and $20 a b$ .

$16 a^{2} + 0 - 25 b^{2}$

Add $16 a^{2}$ and $0$ .

$16 a^{2} - 25 b^{2}$