Simplify (x+9)-(2x-3)^2

$(x + 9) - {(2 x - 3)}^{2}$

Simplify each term.

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

$x + 9 - ((2 x - 3) (2 x - 3))$

Expand $(2 x - 3) (2 x - 3)$ using the FOIL Method.

Apply the distributive property.

$x + 9 - (2 x (2 x - 3) - 3 (2 x - 3))$

Apply the distributive property.

$x + 9 - (2 x (2 x) + 2 x \cdot - 3 - 3 (2 x - 3))$

Apply the distributive property.

$x + 9 - (2 x (2 x) + 2 x \cdot - 3 - 3 (2 x) - 3 \cdot - 3)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$x + 9 - (2 \cdot 2 x \cdot x + 2 x \cdot - 3 - 3 (2 x) - 3 \cdot - 3)$

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

Move $x$ .

$x + 9 - (2 \cdot 2 (x \cdot x) + 2 x \cdot - 3 - 3 (2 x) - 3 \cdot - 3)$

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

$x + 9 - (4 x^{2} + 2 x \cdot - 3 - 3 (2 x) - 3 \cdot - 3)$

Multiply $- 3$ by $2$ .

$x + 9 - (4 x^{2} - 6 x - 3 (2 x) - 3 \cdot - 3)$

Multiply $2$ by $- 3$ .

$x + 9 - (4 x^{2} - 6 x - 6 x - 3 \cdot - 3)$

Multiply $- 3$ by $- 3$ .

$x + 9 - (4 x^{2} - 6 x - 6 x + 9)$

Subtract $6 x$ from $- 6 x$ .

$x + 9 - (4 x^{2} - 12 x + 9)$

Apply the distributive property.

$x + 9 - (4 x^{2}) - (- 12 x) - 1 \cdot 9$

Simplify.

Multiply $4$ by $- 1$ .

$x + 9 - 4 x^{2} - (- 12 x) - 1 \cdot 9$

Multiply $- 12$ by $- 1$ .

$x + 9 - 4 x^{2} + 12 x - 1 \cdot 9$

Multiply $- 1$ by $9$ .

$x + 9 - 4 x^{2} + 12 x - 9$

Simplify by adding terms.

Combine the opposite terms in $x + 9 - 4 x^{2} + 12 x - 9$ .

Subtract $9$ from $9$ .

$x - 4 x^{2} + 12 x + 0$

Add $x - 4 x^{2} + 12 x$ and $0$ .

$x - 4 x^{2} + 12 x$

Add $x$ and $12 x$ .

$- 4 x^{2} + 13 x$

Simplify (x+9)-(2x-3)^2

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