Simplify (2x+7)(2x-7)

$(2 x + 7) (2 x - 7)$

Step 1

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

Apply the distributive property.

$2 x (2 x - 7) + 7 (2 x - 7)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot - 7 + 7 (2 x - 7)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot - 7 + 7 (2 x) + 7 \cdot - 7$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x \cdot - 7 + 7 (2 x) + 7 \cdot - 7$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x \cdot - 7 + 7 (2 x) + 7 \cdot - 7$

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Multiply $- 7$ by $2$ .

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

Multiply $2$ by $7$ .

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

Multiply $7$ by $- 7$ .

$4 x^{2} - 14 x + 14 x - 49$

Add $- 14 x$ and $14 x$ .

$4 x^{2} + 0 - 49$

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

$4 x^{2} - 49$