Algebra Examples

$x^{2} + \frac{1}{2} (20 x^{2} - 10 x + 6) + 2 x$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$x^{2} + \frac{1}{2} (20 x^{2}) + \frac{1}{2} (- 10 x) + \frac{1}{2} \cdot 6 + 2 x$

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 $20 x^{2}$ .

$x^{2} + \frac{1}{2} (2 (10 x^{2})) + \frac{1}{2} (- 10 x) + \frac{1}{2} \cdot 6 + 2 x$

Step 1.2.1.2

Cancel the common factor.

$x^{2} + \frac{1}{2} (2 (10 x^{2})) + \frac{1}{2} (- 10 x) + \frac{1}{2} \cdot 6 + 2 x$

Step 1.2.1.3

Rewrite the expression.

$x^{2} + 10 x^{2} + \frac{1}{2} (- 10 x) + \frac{1}{2} \cdot 6 + 2 x$

Step 1.2.2

Cancel the common factor of $2$ .

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Step 1.2.2.1

Factor $2$ out of $- 10 x$ .

$x^{2} + 10 x^{2} + \frac{1}{2} (2 (- 5 x)) + \frac{1}{2} \cdot 6 + 2 x$

Step 1.2.2.2

Cancel the common factor.

$x^{2} + 10 x^{2} + \frac{1}{2} (2 (- 5 x)) + \frac{1}{2} \cdot 6 + 2 x$

Step 1.2.2.3

Rewrite the expression.

$x^{2} + 10 x^{2} - 5 x + \frac{1}{2} \cdot 6 + 2 x$

Step 1.2.3

Cancel the common factor of $2$ .

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Step 1.2.3.1

Factor $2$ out of $6$ .

$x^{2} + 10 x^{2} - 5 x + \frac{1}{2} \cdot (2 (3)) + 2 x$

Step 1.2.3.2

Cancel the common factor.

$x^{2} + 10 x^{2} - 5 x + \frac{1}{2} \cdot (2 \cdot 3) + 2 x$

Step 1.2.3.3

Rewrite the expression.

$x^{2} + 10 x^{2} - 5 x + 3 + 2 x$

Step 2

Simplify by adding terms.

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Step 2.1

Add $x^{2}$ and $10 x^{2}$ .

$11 x^{2} - 5 x + 3 + 2 x$

Step 2.2

Add $- 5 x$ and $2 x$ .

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