Simplify (5x+7)(5x-7)

$(5 x + 7) (5 x - 7)$

Step 1

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

Apply the distributive property.

$5 x (5 x - 7) + 7 (5 x - 7)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot - 7 + 7 (5 x - 7)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot - 7 + 7 (5 x) + 7 \cdot - 7$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 x \cdot x + 5 x \cdot - 7 + 7 (5 x) + 7 \cdot - 7$

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

Move $x$ .

$5 \cdot 5 (x \cdot x) + 5 x \cdot - 7 + 7 (5 x) + 7 \cdot - 7$

Multiply $x$ by $x$ .

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

Multiply $5$ by $5$ .

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

Multiply $- 7$ by $5$ .

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

Multiply $5$ by $7$ .

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

Multiply $7$ by $- 7$ .

$25 x^{2} - 35 x + 35 x - 49$

Add $- 35 x$ and $35 x$ .

$25 x^{2} + 0 - 49$

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

$25 x^{2} - 49$