Solve (-a^2/2+5)(-a^4/2-5)

$$( - \frac { a ^ { 2 } } { 2 } + 5 ) ( - \frac { a ^ { 4 } } { 2 } - 5 )$$

Evaluate

$$-\frac{\left(10-a^{2}\right)\left(a^{4}+10\right)}{4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{2}{2}.

$$\left(-\frac{a^{2}}{2}+\frac{5\times 2}{2}\right)\left(-\frac{a^{4}}{2}-5\right)$$

Since -\frac{a^{2}}{2} and \frac{5\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{-a^{2}+5\times 2}{2}\left(-\frac{a^{4}}{2}-5\right)$$

Do the multiplications in -a^{2}+5\times 2.

$$\frac{-a^{2}+10}{2}\left(-\frac{a^{4}}{2}-5\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{2}{2}.

$$\frac{-a^{2}+10}{2}\left(-\frac{a^{4}}{2}-\frac{5\times 2}{2}\right)$$

Since -\frac{a^{4}}{2} and \frac{5\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-a^{2}+10}{2}\times \frac{-a^{4}-5\times 2}{2}$$

Do the multiplications in -a^{4}-5\times 2.

$$\frac{-a^{2}+10}{2}\times \frac{-a^{4}-10}{2}$$

Multiply \frac{-a^{2}+10}{2} times \frac{-a^{4}-10}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(-a^{2}+10\right)\left(-a^{4}-10\right)}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\left(-a^{2}+10\right)\left(-a^{4}-10\right)}{4}$$

Use the distributive property to multiply -a^{2}+10 by -a^{4}-10.

$$\frac{a^{6}+10a^{2}-10a^{4}-100}{4}$$

Expand

$$\frac{a^{6}}{4}-\frac{5a^{4}}{2}+\frac{5a^{2}}{2}-25$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{2}{2}.

$$\left(-\frac{a^{2}}{2}+\frac{5\times 2}{2}\right)\left(-\frac{a^{4}}{2}-5\right)$$

Since -\frac{a^{2}}{2} and \frac{5\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{-a^{2}+5\times 2}{2}\left(-\frac{a^{4}}{2}-5\right)$$

Do the multiplications in -a^{2}+5\times 2.

$$\frac{-a^{2}+10}{2}\left(-\frac{a^{4}}{2}-5\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{2}{2}.

$$\frac{-a^{2}+10}{2}\left(-\frac{a^{4}}{2}-\frac{5\times 2}{2}\right)$$

Since -\frac{a^{4}}{2} and \frac{5\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-a^{2}+10}{2}\times \frac{-a^{4}-5\times 2}{2}$$

Do the multiplications in -a^{4}-5\times 2.

$$\frac{-a^{2}+10}{2}\times \frac{-a^{4}-10}{2}$$

Multiply \frac{-a^{2}+10}{2} times \frac{-a^{4}-10}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(-a^{2}+10\right)\left(-a^{4}-10\right)}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\left(-a^{2}+10\right)\left(-a^{4}-10\right)}{4}$$

Use the distributive property to multiply -a^{2}+10 by -a^{4}-10.

$$\frac{a^{6}+10a^{2}-10a^{4}-100}{4}$$