Simplify (3x-7)(3x+7)

$(3 x - 7) (3 x + 7)$

Step 1

Expand $(3 x - 7) (3 x + 7)$ using the FOIL Method.

Apply the distributive property.

$3 x (3 x + 7) - 7 (3 x + 7)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot 7 - 7 (3 x + 7)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot 7 - 7 (3 x) - 7 \cdot 7$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x + 3 x \cdot 7 - 7 (3 x) - 7 \cdot 7$

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

Move $x$ .

$3 \cdot 3 (x \cdot x) + 3 x \cdot 7 - 7 (3 x) - 7 \cdot 7$

Multiply $x$ by $x$ .

$3 \cdot 3 x^{2} + 3 x \cdot 7 - 7 (3 x) - 7 \cdot 7$

Multiply $3$ by $3$ .

$9 x^{2} + 3 x \cdot 7 - 7 (3 x) - 7 \cdot 7$

Multiply $7$ by $3$ .

$9 x^{2} + 21 x - 7 (3 x) - 7 \cdot 7$

Multiply $3$ by $- 7$ .

$9 x^{2} + 21 x - 21 x - 7 \cdot 7$

Multiply $- 7$ by $7$ .

$9 x^{2} + 21 x - 21 x - 49$

Subtract $21 x$ from $21 x$ .

$9 x^{2} + 0 - 49$

Add $9 x^{2}$ and $0$ .

$9 x^{2} - 49$