Simplify (3x-7)^2

${(3 x - 7)}^{2}$

Step 1

Rewrite ${(3 x - 7)}^{2}$ as $(3 x - 7) (3 x - 7)$ .

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

Step 2

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 3

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 $- 21 x$ .

$9 x^{2} - 42 x + 49$