Solve a(9/2)^3-4a*(9/2)^2-9/4+1

$$a ( \frac { 9 } { 2 } ) ^ { 3 } - 4 a \cdot ( \frac { 9 } { 2 } ) ^ { 2 } - \frac { 9 } { 4 } + 1$$

Evaluate

$$\frac{81a}{8}-\frac{5}{4}$$

Solution Steps

Calculate \frac{9}{2} to the power of 3 and get \frac{729}{8}.

$$a\times \frac{729}{8}-4a\times \left(\frac{9}{2}\right)^{2}-\frac{9}{4}+1$$

Calculate \frac{9}{2} to the power of 2 and get \frac{81}{4}.

$$a\times \frac{729}{8}-4a\times \frac{81}{4}-\frac{9}{4}+1$$

Cancel out 4 and 4.

$$a\times \frac{729}{8}-81a-\frac{9}{4}+1$$

Combine a\times \frac{729}{8} and -81a to get \frac{81}{8}a.

$$\frac{81}{8}a-\frac{9}{4}+1$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{81}{8}a-\frac{9}{4}+\frac{4}{4}$$

Since -\frac{9}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{81}{8}a+\frac{-9+4}{4}$$

Add -9 and 4 to get -5.

$$\frac{81}{8}a-\frac{5}{4}$$

Factor

$$\frac{81a-10}{8}$$

Solution Steps

Factor out \frac{1}{8}.

$$\frac{81a-10}{8}$$

Consider 729a-648a-18+8. Multiply and combine like terms.

$$81a-10$$

Rewrite the complete factored expression.

$$\frac{81a-10}{8}$$