Simplify (4x+7)(4x-7)

$(4 x + 7) (4 x - 7)$

Step 1

Expand $(4 x + 7) (4 x - 7)$ using the FOIL Method.

Apply the distributive property.

$4 x (4 x - 7) + 7 (4 x - 7)$

Apply the distributive property.

$4 x (4 x) + 4 x \cdot - 7 + 7 (4 x - 7)$

Apply the distributive property.

$4 x (4 x) + 4 x \cdot - 7 + 7 (4 x) + 7 \cdot - 7$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 x \cdot x + 4 x \cdot - 7 + 7 (4 x) + 7 \cdot - 7$

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

Move $x$ .

$4 \cdot 4 (x \cdot x) + 4 x \cdot - 7 + 7 (4 x) + 7 \cdot - 7$

Multiply $x$ by $x$ .

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

Multiply $4$ by $4$ .

$16 x^{2} + 4 x \cdot - 7 + 7 (4 x) + 7 \cdot - 7$

Multiply $- 7$ by $4$ .

$16 x^{2} - 28 x + 7 (4 x) + 7 \cdot - 7$

Multiply $4$ by $7$ .

$16 x^{2} - 28 x + 28 x + 7 \cdot - 7$

Multiply $7$ by $- 7$ .

$16 x^{2} - 28 x + 28 x - 49$

Add $- 28 x$ and $28 x$ .

$16 x^{2} + 0 - 49$

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

$16 x^{2} - 49$