Solve (6-36/8)^2-4(15/4+9-36*6/16+(36/16)^2-4*frac{15}{16})

$$( 6 - \frac { 36 } { 8 } ) ^ { 2 } - 4 ( \frac { 15 } { 4 } + 9 - \frac { 36 \times 6 } { 16 } + ( \frac { 36 } { 16 } ) ^ { 2 } - 4 \times \frac { 15 } { 16 } )$$

Evaluate

$$0$$

Solution Steps

Reduce the fraction \frac{36}{8} to lowest terms by extracting and canceling out 4.

$$\left(6-\frac{9}{2}\right)^{2}-4\left(\frac{15}{4}+9-\frac{36\times 6}{16}+\left(\frac{36}{16}\right)^{2}-4\times \frac{15}{16}\right)$$

Subtract \frac{9}{2} from 6 to get \frac{3}{2}.

$$\left(\frac{3}{2}\right)^{2}-4\left(\frac{15}{4}+9-\frac{36\times 6}{16}+\left(\frac{36}{16}\right)^{2}-4\times \frac{15}{16}\right)$$

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{9}{4}-4\left(\frac{15}{4}+9-\frac{36\times 6}{16}+\left(\frac{36}{16}\right)^{2}-4\times \frac{15}{16}\right)$$

Add \frac{15}{4} and 9 to get \frac{51}{4}.

$$\frac{9}{4}-4\left(\frac{51}{4}-\frac{36\times 6}{16}+\left(\frac{36}{16}\right)^{2}-4\times \frac{15}{16}\right)$$

Multiply 36 and 6 to get 216.

$$\frac{9}{4}-4\left(\frac{51}{4}-\frac{216}{16}+\left(\frac{36}{16}\right)^{2}-4\times \frac{15}{16}\right)$$

Reduce the fraction \frac{216}{16} to lowest terms by extracting and canceling out 8.

$$\frac{9}{4}-4\left(\frac{51}{4}-\frac{27}{2}+\left(\frac{36}{16}\right)^{2}-4\times \frac{15}{16}\right)$$

Subtract \frac{27}{2} from \frac{51}{4} to get -\frac{3}{4}.

$$\frac{9}{4}-4\left(-\frac{3}{4}+\left(\frac{36}{16}\right)^{2}-4\times \frac{15}{16}\right)$$

Reduce the fraction \frac{36}{16} to lowest terms by extracting and canceling out 4.

$$\frac{9}{4}-4\left(-\frac{3}{4}+\left(\frac{9}{4}\right)^{2}-4\times \frac{15}{16}\right)$$

Calculate \frac{9}{4} to the power of 2 and get \frac{81}{16}.

$$\frac{9}{4}-4\left(-\frac{3}{4}+\frac{81}{16}-4\times \frac{15}{16}\right)$$

Add -\frac{3}{4} and \frac{81}{16} to get \frac{69}{16}.

$$\frac{9}{4}-4\left(\frac{69}{16}-4\times \frac{15}{16}\right)$$

Multiply 4 and \frac{15}{16} to get \frac{15}{4}.

$$\frac{9}{4}-4\left(\frac{69}{16}-\frac{15}{4}\right)$$

Subtract \frac{15}{4} from \frac{69}{16} to get \frac{9}{16}.

$$\frac{9}{4}-4\times \frac{9}{16}$$

Multiply 4 and \frac{9}{16} to get \frac{9}{4}.

$$\frac{9}{4}-\frac{9}{4}$$

Subtract \frac{9}{4} from \frac{9}{4} to get 0.

$$0$$

Factor

$$0$$