Simplify (9x-7)^2

${(9 x - 7)}^{2}$

Step 1

Rewrite ${(9 x - 7)}^{2}$ as $(9 x - 7) (9 x - 7)$ .

$(9 x - 7) (9 x - 7)$

Step 2

Expand $(9 x - 7) (9 x - 7)$ using the FOIL Method.

Apply the distributive property.

$9 x (9 x - 7) - 7 (9 x - 7)$

Apply the distributive property.

$9 x (9 x) + 9 x \cdot - 7 - 7 (9 x - 7)$

Apply the distributive property.

$9 x (9 x) + 9 x \cdot - 7 - 7 (9 x) - 7 \cdot - 7$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$9 \cdot 9 x \cdot x + 9 x \cdot - 7 - 7 (9 x) - 7 \cdot - 7$

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

Move $x$ .

$9 \cdot 9 (x \cdot x) + 9 x \cdot - 7 - 7 (9 x) - 7 \cdot - 7$

Multiply $x$ by $x$ .

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

Multiply $9$ by $9$ .

$81 x^{2} + 9 x \cdot - 7 - 7 (9 x) - 7 \cdot - 7$

Multiply $- 7$ by $9$ .

$81 x^{2} - 63 x - 7 (9 x) - 7 \cdot - 7$

Multiply $9$ by $- 7$ .

$81 x^{2} - 63 x - 63 x - 7 \cdot - 7$

Multiply $- 7$ by $- 7$ .

$81 x^{2} - 63 x - 63 x + 49$

Subtract $63 x$ from $- 63 x$ .

$81 x^{2} - 126 x + 49$