Simplify (2x-9)^2

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

Step 1

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

$(2 x - 9) (2 x - 9)$

Step 2

Expand $(2 x - 9) (2 x - 9)$ using the FOIL Method.

Apply the distributive property.

$2 x (2 x - 9) - 9 (2 x - 9)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot - 9 - 9 (2 x - 9)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot - 9 - 9 (2 x) - 9 \cdot - 9$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x \cdot - 9 - 9 (2 x) - 9 \cdot - 9$

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

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x \cdot - 9 - 9 (2 x) - 9 \cdot - 9$

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

$4 x^{2} + 2 x \cdot - 9 - 9 (2 x) - 9 \cdot - 9$

Multiply $- 9$ by $2$ .

$4 x^{2} - 18 x - 9 (2 x) - 9 \cdot - 9$

Multiply $2$ by $- 9$ .

$4 x^{2} - 18 x - 18 x - 9 \cdot - 9$

Multiply $- 9$ by $- 9$ .

$4 x^{2} - 18 x - 18 x + 81$

Subtract $18 x$ from $- 18 x$ .

$4 x^{2} - 36 x + 81$