Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $x$ by $x$ .

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

Step 1.3.1.2

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

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

Step 1.3.1.3

Multiply $- 12$ by $- 12$ .

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

Step 1.3.2

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

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

Step 1.4

Apply the distributive property.

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

Step 1.5

Multiply $- 1$ by $- 144$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

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

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Step 2.1.1

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

$- 24 x + 144 + 0 + 144$

Step 2.1.2

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

$- 24 x + 144 + 144$

Step 2.2

Add $144$ and $144$ .

$- 24 x + 288$