Solve -frac{3}4^2-[20/2-5/6b^2+21/3a^2-3/4ab+frac{1}{6}b^2-frac{1}{3}b^2-2ab

$$- \frac { 3 } { 4 } ^ { 2 } - \frac { [ 20 } { 2 } - \frac { 5 } { 6 } b ^ { 2 } + 2 \frac { 1 } { 3 } a ^ { 2 } - \frac { 3 } { 4 } a b + \frac { 1 } { 6 } b ^ { 2 } - \frac { 1 } { 3 } b ^ { 2 } - 2 a b$$

Evaluate

$$\frac{11ab}{4}-\frac{7a^{2}}{3}+b^{2}-\frac{169}{16}$$

Solution Steps

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$-\frac{9}{16}-\left(\frac{20}{2}-\frac{5}{6}b^{2}+\frac{2\times 3+1}{3}a^{2}-\frac{3}{4}ab+\frac{1}{6}b^{2}-\frac{1}{3}b^{2}-2ab\right)$$

Divide 20 by 2 to get 10.

$$-\frac{9}{16}-\left(10-\frac{5}{6}b^{2}+\frac{2\times 3+1}{3}a^{2}-\frac{3}{4}ab+\frac{1}{6}b^{2}-\frac{1}{3}b^{2}-2ab\right)$$

Multiply 2 and 3 to get 6.

$$-\frac{9}{16}-\left(10-\frac{5}{6}b^{2}+\frac{6+1}{3}a^{2}-\frac{3}{4}ab+\frac{1}{6}b^{2}-\frac{1}{3}b^{2}-2ab\right)$$

Add 6 and 1 to get 7.

$$-\frac{9}{16}-\left(10-\frac{5}{6}b^{2}+\frac{7}{3}a^{2}-\frac{3}{4}ab+\frac{1}{6}b^{2}-\frac{1}{3}b^{2}-2ab\right)$$

Combine -\frac{5}{6}b^{2} and \frac{1}{6}b^{2} to get -\frac{2}{3}b^{2}.

$$-\frac{9}{16}-\left(10-\frac{2}{3}b^{2}+\frac{7}{3}a^{2}-\frac{3}{4}ab-\frac{1}{3}b^{2}-2ab\right)$$

Combine -\frac{2}{3}b^{2} and -\frac{1}{3}b^{2} to get -b^{2}.

$$-\frac{9}{16}-\left(10-b^{2}+\frac{7}{3}a^{2}-\frac{3}{4}ab-2ab\right)$$

Combine -\frac{3}{4}ab and -2ab to get -\frac{11}{4}ab.

$$-\frac{9}{16}-\left(10-b^{2}+\frac{7}{3}a^{2}-\frac{11}{4}ab\right)$$

To find the opposite of 10-b^{2}+\frac{7}{3}a^{2}-\frac{11}{4}ab, find the opposite of each term.

$$-\frac{9}{16}-10+b^{2}-\frac{7}{3}a^{2}+\frac{11}{4}ab$$

Subtract 10 from -\frac{9}{16} to get -\frac{169}{16}.

$$-\frac{169}{16}+b^{2}-\frac{7}{3}a^{2}+\frac{11}{4}ab$$

Expand

$$\frac{11ab}{4}-\frac{7a^{2}}{3}+b^{2}-\frac{169}{16}$$

Solution Steps

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$-\frac{9}{16}-\left(\frac{20}{2}-\frac{5}{6}b^{2}+\frac{2\times 3+1}{3}a^{2}-\frac{3}{4}ab+\frac{1}{6}b^{2}-\frac{1}{3}b^{2}-2ab\right)$$

Divide 20 by 2 to get 10.

$$-\frac{9}{16}-\left(10-\frac{5}{6}b^{2}+\frac{2\times 3+1}{3}a^{2}-\frac{3}{4}ab+\frac{1}{6}b^{2}-\frac{1}{3}b^{2}-2ab\right)$$

Multiply 2 and 3 to get 6.

$$-\frac{9}{16}-\left(10-\frac{5}{6}b^{2}+\frac{6+1}{3}a^{2}-\frac{3}{4}ab+\frac{1}{6}b^{2}-\frac{1}{3}b^{2}-2ab\right)$$

Add 6 and 1 to get 7.

$$-\frac{9}{16}-\left(10-\frac{5}{6}b^{2}+\frac{7}{3}a^{2}-\frac{3}{4}ab+\frac{1}{6}b^{2}-\frac{1}{3}b^{2}-2ab\right)$$

Combine -\frac{5}{6}b^{2} and \frac{1}{6}b^{2} to get -\frac{2}{3}b^{2}.

$$-\frac{9}{16}-\left(10-\frac{2}{3}b^{2}+\frac{7}{3}a^{2}-\frac{3}{4}ab-\frac{1}{3}b^{2}-2ab\right)$$

Combine -\frac{2}{3}b^{2} and -\frac{1}{3}b^{2} to get -b^{2}.

$$-\frac{9}{16}-\left(10-b^{2}+\frac{7}{3}a^{2}-\frac{3}{4}ab-2ab\right)$$

Combine -\frac{3}{4}ab and -2ab to get -\frac{11}{4}ab.

$$-\frac{9}{16}-\left(10-b^{2}+\frac{7}{3}a^{2}-\frac{11}{4}ab\right)$$

To find the opposite of 10-b^{2}+\frac{7}{3}a^{2}-\frac{11}{4}ab, find the opposite of each term.

$$-\frac{9}{16}-10+b^{2}-\frac{7}{3}a^{2}+\frac{11}{4}ab$$

Subtract 10 from -\frac{9}{16} to get -\frac{169}{16}.

$$-\frac{169}{16}+b^{2}-\frac{7}{3}a^{2}+\frac{11}{4}ab$$