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

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

Evaluate

$$\frac{a^{8}}{4}-25$$

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Multiply 2 and 2 to get 4.

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

Consider \left(-a^{4}+10\right)\left(-a^{4}-10\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 10.

$$\frac{\left(-a^{4}\right)^{2}-100}{4}$$

Expand \left(-a^{4}\right)^{2}.

$$\frac{\left(-1\right)^{2}\left(a^{4}\right)^{2}-100}{4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\left(-1\right)^{2}a^{8}-100}{4}$$

Calculate -1 to the power of 2 and get 1.

$$\frac{1a^{8}-100}{4}$$

For any term t, t\times 1=t and 1t=t.

$$\frac{a^{8}-100}{4}$$

Expand

$$\frac{a^{8}}{4}-25$$

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Multiply 2 and 2 to get 4.

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

Consider \left(-a^{4}+10\right)\left(-a^{4}-10\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 10.

$$\frac{\left(-a^{4}\right)^{2}-100}{4}$$

Expand \left(-a^{4}\right)^{2}.

$$\frac{\left(-1\right)^{2}\left(a^{4}\right)^{2}-100}{4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\left(-1\right)^{2}a^{8}-100}{4}$$

Calculate -1 to the power of 2 and get 1.

$$\frac{1a^{8}-100}{4}$$

For any term t, t\times 1=t and 1t=t.

$$\frac{a^{8}-100}{4}$$