Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Multiply $4$ by $2$ .

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

Step 1.3

Multiply $- 2$ by $2$ .

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

Step 1.4

Apply the distributive property.

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

Step 1.5

Multiply $- 6$ by $- 3$ .

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

Step 1.6

Multiply $- 3$ by $4$ .

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

Step 1.7

Apply the distributive property.

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

Step 1.8

Multiply $k$ by $k$ by adding the exponents.

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Step 1.8.1

Move $k$ .

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

Step 1.8.2

Multiply $k$ by $k$ .

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

Step 1.9

Multiply $- 1$ by $2$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Subtract $2 k$ from $- 4 k$ .

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