Algebra Examples

$3 x (x - 12 x) + 3 x^{2} - 2 {(x - 2)}^{2}$

Step 1

Simplify each term.

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Step 1.1

Subtract $12 x$ from $x$ .

$3 x (- 11 x) + 3 x^{2} - 2 {(x - 2)}^{2}$

Step 1.2

Rewrite using the commutative property of multiplication.

$3 \cdot - 11 x \cdot x + 3 x^{2} - 2 {(x - 2)}^{2}$

Step 1.3

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

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Step 1.3.1

Move $x$ .

$3 \cdot - 11 (x \cdot x) + 3 x^{2} - 2 {(x - 2)}^{2}$

Step 1.3.2

Multiply $x$ by $x$ .

$3 \cdot - 11 x^{2} + 3 x^{2} - 2 {(x - 2)}^{2}$

Step 1.4

Multiply $3$ by $- 11$ .

$- 33 x^{2} + 3 x^{2} - 2 {(x - 2)}^{2}$

Step 1.5

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

$- 33 x^{2} + 3 x^{2} - 2 ((x - 2) (x - 2))$

Step 1.6

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

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Step 1.6.1

Apply the distributive property.

$- 33 x^{2} + 3 x^{2} - 2 (x (x - 2) - 2 (x - 2))$

Step 1.6.2

Apply the distributive property.

$- 33 x^{2} + 3 x^{2} - 2 (x \cdot x + x \cdot - 2 - 2 (x - 2))$

Step 1.6.3

Apply the distributive property.

$- 33 x^{2} + 3 x^{2} - 2 (x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2)$

Step 1.7

Simplify and combine like terms.

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Step 1.7.1

Simplify each term.

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Step 1.7.1.1

Multiply $x$ by $x$ .

$- 33 x^{2} + 3 x^{2} - 2 (x^{2} + x \cdot - 2 - 2 x - 2 \cdot - 2)$

Step 1.7.1.2

Move $- 2$ to the left of $x$ .

$- 33 x^{2} + 3 x^{2} - 2 (x^{2} - 2 \cdot x - 2 x - 2 \cdot - 2)$

Step 1.7.1.3

Multiply $- 2$ by $- 2$ .

$- 33 x^{2} + 3 x^{2} - 2 (x^{2} - 2 x - 2 x + 4)$

Step 1.7.2

Subtract $2 x$ from $- 2 x$ .

$- 33 x^{2} + 3 x^{2} - 2 (x^{2} - 4 x + 4)$

Step 1.8

Apply the distributive property.

$- 33 x^{2} + 3 x^{2} - 2 x^{2} - 2 (- 4 x) - 2 \cdot 4$

Step 1.9

Simplify.

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Step 1.9.1

Multiply $- 4$ by $- 2$ .

$- 33 x^{2} + 3 x^{2} - 2 x^{2} + 8 x - 2 \cdot 4$

Step 1.9.2

Multiply $- 2$ by $4$ .

$- 33 x^{2} + 3 x^{2} - 2 x^{2} + 8 x - 8$

Step 2

Simplify by adding terms.

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Step 2.1

Add $- 33 x^{2}$ and $3 x^{2}$ .

$- 30 x^{2} - 2 x^{2} + 8 x - 8$

Step 2.2

Subtract $2 x^{2}$ from $- 30 x^{2}$ .

$- 32 x^{2} + 8 x - 8$