Solve -a^{6}+a^2*a^3+a^8div(-a^2)

$$- a ^ { 6 } + a ^ { 2 } \cdot a ^ { 3 } + a ^ { 8 } \div ( - a ^ { 2 } )$$

Evaluate

$$\left(1-2a\right)a^{5}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$-a^{6}+a^{5}+\frac{a^{8}}{-a^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -a^{6}+a^{5} times \frac{-a^{2}}{-a^{2}}.

$$\frac{\left(-a^{6}+a^{5}\right)\left(-1\right)a^{2}}{-a^{2}}+\frac{a^{8}}{-a^{2}}$$

Since \frac{\left(-a^{6}+a^{5}\right)\left(-1\right)a^{2}}{-a^{2}} and \frac{a^{8}}{-a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(-a^{6}+a^{5}\right)\left(-1\right)a^{2}+a^{8}}{-a^{2}}$$

Do the multiplications in \left(-a^{6}+a^{5}\right)\left(-1\right)a^{2}+a^{8}.

$$\frac{a^{8}-a^{7}+a^{8}}{-a^{2}}$$

Combine like terms in a^{8}-a^{7}+a^{8}.

$$\frac{2a^{8}-a^{7}}{-a^{2}}$$

Factor the expressions that are not already factored in \frac{2a^{8}-a^{7}}{-a^{2}}.

$$\frac{\left(2a-1\right)a^{7}}{-a^{2}}$$

Cancel out a^{2} in both numerator and denominator.

$$\frac{\left(2a-1\right)a^{5}}{-1}$$

Anything divided by -1 gives its opposite.

$$-\left(2a-1\right)a^{5}$$

Use the distributive property to multiply -1 by 2a-1.

$$\left(-2a+1\right)a^{5}$$

Use the distributive property to multiply -2a+1 by a^{5}.

$$-2a^{6}+a^{5}$$

Factor

$$\left(1-2a\right)a^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$factor(-a^{6}+a^{5}+\frac{a^{8}}{-a^{2}})$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -a^{6}+a^{5} times \frac{-a^{2}}{-a^{2}}.

$$factor(\frac{\left(-a^{6}+a^{5}\right)\left(-1\right)a^{2}}{-a^{2}}+\frac{a^{8}}{-a^{2}})$$

Since \frac{\left(-a^{6}+a^{5}\right)\left(-1\right)a^{2}}{-a^{2}} and \frac{a^{8}}{-a^{2}} have the same denominator, add them by adding their numerators.

$$factor(\frac{\left(-a^{6}+a^{5}\right)\left(-1\right)a^{2}+a^{8}}{-a^{2}})$$

Do the multiplications in \left(-a^{6}+a^{5}\right)\left(-1\right)a^{2}+a^{8}.

$$factor(\frac{a^{8}-a^{7}+a^{8}}{-a^{2}})$$

Combine like terms in a^{8}-a^{7}+a^{8}.

$$factor(\frac{2a^{8}-a^{7}}{-a^{2}})$$

Factor the expressions that are not already factored in \frac{2a^{8}-a^{7}}{-a^{2}}.

$$factor(\frac{\left(2a-1\right)a^{7}}{-a^{2}})$$

Cancel out a^{2} in both numerator and denominator.

$$factor(\frac{\left(2a-1\right)a^{5}}{-1})$$

Anything divided by -1 gives its opposite.

$$factor(-\left(2a-1\right)a^{5})$$

Use the distributive property to multiply -1 by 2a-1.

$$factor(\left(-2a+1\right)a^{5})$$

Use the distributive property to multiply -2a+1 by a^{5}.

$$factor(-2a^{6}+a^{5})$$

Factor out a^{5}.

$$a^{5}\left(-2a+1\right)$$