Algebra Examples

$(5 x^{2} + 7 x) - \frac{1}{2} (10 x^{2} - 4)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$5 x^{2} + 7 x - \frac{1}{2} (10 x^{2}) - \frac{1}{2} \cdot - 4$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$5 x^{2} + 7 x + \frac{- 1}{2} (10 x^{2}) - \frac{1}{2} \cdot - 4$

Step 1.2.2

Factor $2$ out of $10 x^{2}$ .

$5 x^{2} + 7 x + \frac{- 1}{2} (2 (5 x^{2})) - \frac{1}{2} \cdot - 4$

Step 1.2.3

Cancel the common factor.

$5 x^{2} + 7 x + \frac{- 1}{2} (2 (5 x^{2})) - \frac{1}{2} \cdot - 4$

Step 1.2.4

Rewrite the expression.

$5 x^{2} + 7 x - 1 (5 x^{2}) - \frac{1}{2} \cdot - 4$

Step 1.3

Multiply $5$ by $- 1$ .

$5 x^{2} + 7 x - 5 x^{2} - \frac{1}{2} \cdot - 4$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$5 x^{2} + 7 x - 5 x^{2} + \frac{- 1}{2} \cdot - 4$

Step 1.4.2

Factor $2$ out of $- 4$ .

$5 x^{2} + 7 x - 5 x^{2} + \frac{- 1}{2} \cdot (2 (- 2))$

Step 1.4.3

Cancel the common factor.

$5 x^{2} + 7 x - 5 x^{2} + \frac{- 1}{2} \cdot (2 \cdot - 2)$

Step 1.4.4

Rewrite the expression.

$5 x^{2} + 7 x - 5 x^{2} - 1 \cdot - 2$

Step 1.5

Multiply $- 1$ by $- 2$ .

$5 x^{2} + 7 x - 5 x^{2} + 2$

Step 2

Combine the opposite terms in $5 x^{2} + 7 x - 5 x^{2} + 2$ .

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Step 2.1

Subtract $5 x^{2}$ from $5 x^{2}$ .

$7 x + 0 + 2$

Step 2.2

Add $7 x$ and $0$ .

$7 x + 2$