Simplify (5x^2+7x)-1/2(10x^2-4)

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

Step 1

Simplify each term.

Apply the distributive property.

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

Cancel the common factor of $2$ .

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $5$ by $- 1$ .

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

Cancel the common factor of $2$ .

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

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

Factor $2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 1$ by $- 2$ .

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

Step 2

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

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

$7 x + 0 + 2$

Add $7 x$ and $0$ .

$7 x + 2$