Simplify (x-12)^2-(x^2-144)

${(x - 12)}^{2} - (x^{2} - 144)$

Step 1

Simplify each term.

Rewrite ${(x - 12)}^{2}$ as $(x - 12) (x - 12)$ .

$(x - 12) (x - 12) - (x^{2} - 144)$

Expand $(x - 12) (x - 12)$ using the FOIL Method.

Apply the distributive property.

$x (x - 12) - 12 (x - 12) - (x^{2} - 144)$

Apply the distributive property.

$x \cdot x + x \cdot - 12 - 12 (x - 12) - (x^{2} - 144)$

Apply the distributive property.

$x \cdot x + x \cdot - 12 - 12 x - 12 \cdot - 12 - (x^{2} - 144)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 12 - 12 x - 12 \cdot - 12 - (x^{2} - 144)$

Move $- 12$ to the left of $x$ .

$x^{2} - 12 \cdot x - 12 x - 12 \cdot - 12 - (x^{2} - 144)$

Multiply $- 12$ by $- 12$ .

$x^{2} - 12 x - 12 x + 144 - (x^{2} - 144)$

Subtract $12 x$ from $- 12 x$ .

$x^{2} - 24 x + 144 - (x^{2} - 144)$

Apply the distributive property.

$x^{2} - 24 x + 144 - x^{2} - - 144$

Multiply $- 1$ by $- 144$ .

$x^{2} - 24 x + 144 - x^{2} + 144$

Step 2

Simplify by adding terms.

Combine the opposite terms in $x^{2} - 24 x + 144 - x^{2} + 144$ .

Subtract $x^{2}$ from $x^{2}$ .

$- 24 x + 144 + 0 + 144$

Add $- 24 x + 144$ and $0$ .

$- 24 x + 144 + 144$

Add $144$ and $144$ .

$- 24 x + 288$