Simplify (2a+7b)(2a-7b)

$(2 a + 7 b) (2 a - 7 b)$

Step 1

Expand $(2 a + 7 b) (2 a - 7 b)$ using the FOIL Method.

Apply the distributive property.

$2 a (2 a - 7 b) + 7 b (2 a - 7 b)$

Apply the distributive property.

$2 a (2 a) + 2 a (- 7 b) + 7 b (2 a - 7 b)$

Apply the distributive property.

$2 a (2 a) + 2 a (- 7 b) + 7 b (2 a) + 7 b (- 7 b)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 a \cdot a + 2 a (- 7 b) + 7 b (2 a) + 7 b (- 7 b)$

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

Move $a$ .

$2 \cdot 2 (a \cdot a) + 2 a (- 7 b) + 7 b (2 a) + 7 b (- 7 b)$

Multiply $a$ by $a$ .

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

Multiply $2$ by $2$ .

$4 a^{2} + 2 a (- 7 b) + 7 b (2 a) + 7 b (- 7 b)$

Rewrite using the commutative property of multiplication.

$4 a^{2} + 2 \cdot - 7 a b + 7 b (2 a) + 7 b (- 7 b)$

Multiply $2$ by $- 7$ .

$4 a^{2} - 14 a b + 7 b (2 a) + 7 b (- 7 b)$

Rewrite using the commutative property of multiplication.

$4 a^{2} - 14 a b + 7 \cdot 2 b a + 7 b (- 7 b)$

Multiply $7$ by $2$ .

$4 a^{2} - 14 a b + 14 b a + 7 b (- 7 b)$

Rewrite using the commutative property of multiplication.

$4 a^{2} - 14 a b + 14 b a + 7 \cdot - 7 b \cdot b$

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

Move $b$ .

$4 a^{2} - 14 a b + 14 b a + 7 \cdot - 7 (b \cdot b)$

Multiply $b$ by $b$ .

$4 a^{2} - 14 a b + 14 b a + 7 \cdot - 7 b^{2}$

Multiply $7$ by $- 7$ .

$4 a^{2} - 14 a b + 14 b a - 49 b^{2}$

Add $- 14 a b$ and $14 b a$ .

Move $b$ .

$4 a^{2} - 14 a b + 14 a b - 49 b^{2}$

Add $- 14 a b$ and $14 a b$ .

$4 a^{2} + 0 - 49 b^{2}$

Add $4 a^{2}$ and $0$ .

$4 a^{2} - 49 b^{2}$