Simplify (4x-9)^2

${(4 x - 9)}^{2}$

Step 1

Rewrite ${(4 x - 9)}^{2}$ as $(4 x - 9) (4 x - 9)$ .

$(4 x - 9) (4 x - 9)$

Step 2

Expand $(4 x - 9) (4 x - 9)$ using the FOIL Method.

Apply the distributive property.

$4 x (4 x - 9) - 9 (4 x - 9)$

Apply the distributive property.

$4 x (4 x) + 4 x \cdot - 9 - 9 (4 x - 9)$

Apply the distributive property.

$4 x (4 x) + 4 x \cdot - 9 - 9 (4 x) - 9 \cdot - 9$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 x \cdot x + 4 x \cdot - 9 - 9 (4 x) - 9 \cdot - 9$

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

Move $x$ .

$4 \cdot 4 (x \cdot x) + 4 x \cdot - 9 - 9 (4 x) - 9 \cdot - 9$

Multiply $x$ by $x$ .

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

Multiply $4$ by $4$ .

$16 x^{2} + 4 x \cdot - 9 - 9 (4 x) - 9 \cdot - 9$

Multiply $- 9$ by $4$ .

$16 x^{2} - 36 x - 9 (4 x) - 9 \cdot - 9$

Multiply $4$ by $- 9$ .

$16 x^{2} - 36 x - 36 x - 9 \cdot - 9$

Multiply $- 9$ by $- 9$ .

$16 x^{2} - 36 x - 36 x + 81$

Subtract $36 x$ from $- 36 x$ .

$16 x^{2} - 72 x + 81$