Simplify x-(3x-8)^2

$x - {(3 x - 8)}^{2}$

Simplify each term.

Rewrite ${(3 x - 8)}^{2}$ as $(3 x - 8) (3 x - 8)$ .

$x - ((3 x - 8) (3 x - 8))$

Expand $(3 x - 8) (3 x - 8)$ using the FOIL Method.

Apply the distributive property.

$x - (3 x (3 x - 8) - 8 (3 x - 8))$

Apply the distributive property.

$x - (3 x (3 x) + 3 x \cdot - 8 - 8 (3 x - 8))$

Apply the distributive property.

$x - (3 x (3 x) + 3 x \cdot - 8 - 8 (3 x) - 8 \cdot - 8)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$x - (3 \cdot 3 x \cdot x + 3 x \cdot - 8 - 8 (3 x) - 8 \cdot - 8)$

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

Move $x$ .

$x - (3 \cdot 3 (x \cdot x) + 3 x \cdot - 8 - 8 (3 x) - 8 \cdot - 8)$

Multiply $x$ by $x$ .

$x - (3 \cdot 3 x^{2} + 3 x \cdot - 8 - 8 (3 x) - 8 \cdot - 8)$

Multiply $3$ by $3$ .

$x - (9 x^{2} + 3 x \cdot - 8 - 8 (3 x) - 8 \cdot - 8)$

Multiply $- 8$ by $3$ .

$x - (9 x^{2} - 24 x - 8 (3 x) - 8 \cdot - 8)$

Multiply $3$ by $- 8$ .

$x - (9 x^{2} - 24 x - 24 x - 8 \cdot - 8)$

Multiply $- 8$ by $- 8$ .

$x - (9 x^{2} - 24 x - 24 x + 64)$

Subtract $24 x$ from $- 24 x$ .

$x - (9 x^{2} - 48 x + 64)$

Apply the distributive property.

$x - (9 x^{2}) - (- 48 x) - 1 \cdot 64$

Simplify.

Multiply $9$ by $- 1$ .

$x - 9 x^{2} - (- 48 x) - 1 \cdot 64$

Multiply $- 48$ by $- 1$ .

$x - 9 x^{2} + 48 x - 1 \cdot 64$

Multiply $- 1$ by $64$ .

$x - 9 x^{2} + 48 x - 64$

Add $x$ and $48 x$ .

$- 9 x^{2} + 49 x - 64$