Simplify (5a+7b)(5a-7b)

$(5 a + 7 b) (5 a - 7 b)$

Step 1

Expand $(5 a + 7 b) (5 a - 7 b)$ using the FOIL Method.

Apply the distributive property.

$5 a (5 a - 7 b) + 7 b (5 a - 7 b)$

Apply the distributive property.

$5 a (5 a) + 5 a (- 7 b) + 7 b (5 a - 7 b)$

Apply the distributive property.

$5 a (5 a) + 5 a (- 7 b) + 7 b (5 a) + 7 b (- 7 b)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 a \cdot a + 5 a (- 7 b) + 7 b (5 a) + 7 b (- 7 b)$

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

Move $a$ .

$5 \cdot 5 (a \cdot a) + 5 a (- 7 b) + 7 b (5 a) + 7 b (- 7 b)$

Multiply $a$ by $a$ .

$5 \cdot 5 a^{2} + 5 a (- 7 b) + 7 b (5 a) + 7 b (- 7 b)$

Multiply $5$ by $5$ .

$25 a^{2} + 5 a (- 7 b) + 7 b (5 a) + 7 b (- 7 b)$

Rewrite using the commutative property of multiplication.

$25 a^{2} + 5 \cdot - 7 a b + 7 b (5 a) + 7 b (- 7 b)$

Multiply $5$ by $- 7$ .

$25 a^{2} - 35 a b + 7 b (5 a) + 7 b (- 7 b)$

Rewrite using the commutative property of multiplication.

$25 a^{2} - 35 a b + 7 \cdot 5 b a + 7 b (- 7 b)$

Multiply $7$ by $5$ .

$25 a^{2} - 35 a b + 35 b a + 7 b (- 7 b)$

Rewrite using the commutative property of multiplication.

$25 a^{2} - 35 a b + 35 b a + 7 \cdot - 7 b \cdot b$

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

Move $b$ .

$25 a^{2} - 35 a b + 35 b a + 7 \cdot - 7 (b \cdot b)$

Multiply $b$ by $b$ .

$25 a^{2} - 35 a b + 35 b a + 7 \cdot - 7 b^{2}$

Multiply $7$ by $- 7$ .

$25 a^{2} - 35 a b + 35 b a - 49 b^{2}$

Add $- 35 a b$ and $35 b a$ .

Move $b$ .

$25 a^{2} - 35 a b + 35 a b - 49 b^{2}$

Add $- 35 a b$ and $35 a b$ .

$25 a^{2} + 0 - 49 b^{2}$

Add $25 a^{2}$ and $0$ .

$25 a^{2} - 49 b^{2}$