Solve x^2-1/5xy+3/8x^2+11/5xy-3/2x^2-frac{8}{10}xy

$$x ^ { 2 } - \frac { 1 } { 5 } x y + \frac { 3 } { 8 } x ^ { 2 } + \frac { 11 } { 5 } x y - \frac { 3 } { 2 } x ^ { 2 } - \frac { 8 } { 10 } x y$$

Evaluate

$$\frac{6xy}{5}-\frac{x^{2}}{8}$$

Solution Steps

Combine x^{2} and \frac{3}{8}x^{2} to get \frac{11}{8}x^{2}.

$$\frac{11}{8}x^{2}-\frac{1}{5}xy+\frac{11}{5}xy-\frac{3}{2}x^{2}-\frac{8}{10}xy$$

Combine -\frac{1}{5}xy and \frac{11}{5}xy to get 2xy.

$$\frac{11}{8}x^{2}+2xy-\frac{3}{2}x^{2}-\frac{8}{10}xy$$

Combine \frac{11}{8}x^{2} and -\frac{3}{2}x^{2} to get -\frac{1}{8}x^{2}.

$$-\frac{1}{8}x^{2}+2xy-\frac{8}{10}xy$$

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{8}x^{2}+2xy-\frac{4}{5}xy$$

Combine 2xy and -\frac{4}{5}xy to get \frac{6}{5}xy.

$$-\frac{1}{8}x^{2}+\frac{6}{5}xy$$

Factor

$$\frac{x\left(48y-5x\right)}{40}$$

Solution Steps

Factor out \frac{1}{40}.

$$\frac{40x^{2}-8xy+15x^{2}+88xy-60x^{2}-32xy}{40}$$

Consider 40x^{2}-8xy+15x^{2}+88xy-60x^{2}-32xy. Factor out x.

$$x\left(40x-8y+15x+88y-60x-32y\right)$$

Consider 40x-8y+15x+88y-60x-32y. Multiply and combine like terms.

$$-5x+48y$$

Rewrite the complete factored expression.

$$\frac{x\left(-5x+48y\right)}{40}$$