Algebra Examples

$\frac{1}{2} (4 x^{2} + 6 x - 2) - 5 (- 3 x^{2} + 2 x + 2)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{1}{2} (4 x^{2}) + \frac{1}{2} (6 x) + \frac{1}{2} \cdot - 2 - 5 (- 3 x^{2} + 2 x + 2)$

Step 1.2

Simplify.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Factor $2$ out of $4 x^{2}$ .

$\frac{1}{2} (2 (2 x^{2})) + \frac{1}{2} (6 x) + \frac{1}{2} \cdot - 2 - 5 (- 3 x^{2} + 2 x + 2)$

Step 1.2.1.2

Cancel the common factor.

$\frac{1}{2} (2 (2 x^{2})) + \frac{1}{2} (6 x) + \frac{1}{2} \cdot - 2 - 5 (- 3 x^{2} + 2 x + 2)$

Step 1.2.1.3

Rewrite the expression.

$2 x^{2} + \frac{1}{2} (6 x) + \frac{1}{2} \cdot - 2 - 5 (- 3 x^{2} + 2 x + 2)$

Step 1.2.2

Cancel the common factor of $2$ .

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Step 1.2.2.1

Factor $2$ out of $6 x$ .

$2 x^{2} + \frac{1}{2} (2 (3 x)) + \frac{1}{2} \cdot - 2 - 5 (- 3 x^{2} + 2 x + 2)$

Step 1.2.2.2

Cancel the common factor.

$2 x^{2} + \frac{1}{2} (2 (3 x)) + \frac{1}{2} \cdot - 2 - 5 (- 3 x^{2} + 2 x + 2)$

Step 1.2.2.3

Rewrite the expression.

$2 x^{2} + 3 x + \frac{1}{2} \cdot - 2 - 5 (- 3 x^{2} + 2 x + 2)$

Step 1.2.3

Cancel the common factor of $2$ .

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Step 1.2.3.1

Factor $2$ out of $- 2$ .

$2 x^{2} + 3 x + \frac{1}{2} \cdot (2 (- 1)) - 5 (- 3 x^{2} + 2 x + 2)$

Step 1.2.3.2

Cancel the common factor.

$2 x^{2} + 3 x + \frac{1}{2} \cdot (2 \cdot - 1) - 5 (- 3 x^{2} + 2 x + 2)$

Step 1.2.3.3

Rewrite the expression.

$2 x^{2} + 3 x - 1 - 5 (- 3 x^{2} + 2 x + 2)$

Step 1.3

Apply the distributive property.

$2 x^{2} + 3 x - 1 - 5 (- 3 x^{2}) - 5 (2 x) - 5 \cdot 2$

Step 1.4

Simplify.

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Step 1.4.1

Multiply $- 3$ by $- 5$ .

$2 x^{2} + 3 x - 1 + 15 x^{2} - 5 (2 x) - 5 \cdot 2$

Step 1.4.2

Multiply $2$ by $- 5$ .

$2 x^{2} + 3 x - 1 + 15 x^{2} - 10 x - 5 \cdot 2$

Step 1.4.3

Multiply $- 5$ by $2$ .

$2 x^{2} + 3 x - 1 + 15 x^{2} - 10 x - 10$

Step 2

Simplify by adding terms.

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Step 2.1

Add $2 x^{2}$ and $15 x^{2}$ .

$17 x^{2} + 3 x - 1 - 10 x - 10$

Step 2.2

Subtract $10 x$ from $3 x$ .

$17 x^{2} - 7 x - 1 - 10$

Step 2.3

Subtract $10$ from $- 1$ .

$17 x^{2} - 7 x - 11$