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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $7$ .

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

Multiply $- 3$ by $3$ .

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

Multiply $7$ by $7$ .

$21 x^{2} - 9 x + 49 x + 7 \cdot - 3$

Multiply $7$ by $- 3$ .

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

Add $- 9 x$ and $49 x$ .

$21 x^{2} + 40 x - 21$