Algebra Examples

$2 (4 x^{2} - 2 x) - 3 (- 6 x^{2} + 4) + 2 x (x - 1)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$2 (4 x^{2}) + 2 (- 2 x) - 3 (- 6 x^{2} + 4) + 2 x (x - 1)$

Step 1.2

Multiply $4$ by $2$ .

$8 x^{2} + 2 (- 2 x) - 3 (- 6 x^{2} + 4) + 2 x (x - 1)$

Step 1.3

Multiply $- 2$ by $2$ .

$8 x^{2} - 4 x - 3 (- 6 x^{2} + 4) + 2 x (x - 1)$

Step 1.4

Apply the distributive property.

$8 x^{2} - 4 x - 3 (- 6 x^{2}) - 3 \cdot 4 + 2 x (x - 1)$

Step 1.5

Multiply $- 6$ by $- 3$ .

$8 x^{2} - 4 x + 18 x^{2} - 3 \cdot 4 + 2 x (x - 1)$

Step 1.6

Multiply $- 3$ by $4$ .

$8 x^{2} - 4 x + 18 x^{2} - 12 + 2 x (x - 1)$

Step 1.7

Apply the distributive property.

$8 x^{2} - 4 x + 18 x^{2} - 12 + 2 x \cdot x + 2 x \cdot - 1$

Step 1.8

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

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Step 1.8.1

Move $x$ .

$8 x^{2} - 4 x + 18 x^{2} - 12 + 2 (x \cdot x) + 2 x \cdot - 1$

Step 1.8.2

Multiply $x$ by $x$ .

$8 x^{2} - 4 x + 18 x^{2} - 12 + 2 x^{2} + 2 x \cdot - 1$

Step 1.9

Multiply $- 1$ by $2$ .

$8 x^{2} - 4 x + 18 x^{2} - 12 + 2 x^{2} - 2 x$

Step 2

Simplify by adding terms.

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Step 2.1

Add $8 x^{2}$ and $18 x^{2}$ .

$26 x^{2} - 4 x - 12 + 2 x^{2} - 2 x$

Step 2.2

Add $26 x^{2}$ and $2 x^{2}$ .

$28 x^{2} - 4 x - 12 - 2 x$

Step 2.3

Subtract $2 x$ from $- 4 x$ .

$28 x^{2} - 6 x - 12$