Solve (4/7y^3-2/5y^2+6y-3/7)-(2/7y^3+frac{3}{5}y^2+frac{4}{5}y-frac{1}{7})

$$( \frac { 4 } { 7 } y ^ { 3 } - \frac { 2 } { 5 } y ^ { 2 } + 6 y - \frac { 3 } { 7 } ) - ( \frac { 2 } { 7 } y ^ { 3 } + \frac { 3 } { 5 } y ^ { 2 } + \frac { 4 } { 5 } y - \frac { 1 } { 7 } )$$

Evaluate

$$\frac{2y^{3}}{7}-y^{2}+\frac{26y}{5}-\frac{2}{7}$$

Solution Steps

To find the opposite of \frac{2}{7}y^{3}+\frac{3}{5}y^{2}+\frac{4}{5}y-\frac{1}{7}, find the opposite of each term.

$$\frac{4}{7}y^{3}-\frac{2}{5}y^{2}+6y-\frac{3}{7}-\frac{2}{7}y^{3}-\frac{3}{5}y^{2}-\frac{4}{5}y+\frac{1}{7}$$

Combine \frac{4}{7}y^{3} and -\frac{2}{7}y^{3} to get \frac{2}{7}y^{3}.

$$\frac{2}{7}y^{3}-\frac{2}{5}y^{2}+6y-\frac{3}{7}-\frac{3}{5}y^{2}-\frac{4}{5}y+\frac{1}{7}$$

Combine -\frac{2}{5}y^{2} and -\frac{3}{5}y^{2} to get -y^{2}.

$$\frac{2}{7}y^{3}-y^{2}+6y-\frac{3}{7}-\frac{4}{5}y+\frac{1}{7}$$

Combine 6y and -\frac{4}{5}y to get \frac{26}{5}y.

$$\frac{2}{7}y^{3}-y^{2}+\frac{26}{5}y-\frac{3}{7}+\frac{1}{7}$$

Add -\frac{3}{7} and \frac{1}{7} to get -\frac{2}{7}.

$$\frac{2}{7}y^{3}-y^{2}+\frac{26}{5}y-\frac{2}{7}$$

Expand

$$\frac{2y^{3}}{7}-y^{2}+\frac{26y}{5}-\frac{2}{7}$$

Solution Steps

To find the opposite of \frac{2}{7}y^{3}+\frac{3}{5}y^{2}+\frac{4}{5}y-\frac{1}{7}, find the opposite of each term.

$$\frac{4}{7}y^{3}-\frac{2}{5}y^{2}+6y-\frac{3}{7}-\frac{2}{7}y^{3}-\frac{3}{5}y^{2}-\frac{4}{5}y+\frac{1}{7}$$

Combine \frac{4}{7}y^{3} and -\frac{2}{7}y^{3} to get \frac{2}{7}y^{3}.

$$\frac{2}{7}y^{3}-\frac{2}{5}y^{2}+6y-\frac{3}{7}-\frac{3}{5}y^{2}-\frac{4}{5}y+\frac{1}{7}$$

Combine -\frac{2}{5}y^{2} and -\frac{3}{5}y^{2} to get -y^{2}.

$$\frac{2}{7}y^{3}-y^{2}+6y-\frac{3}{7}-\frac{4}{5}y+\frac{1}{7}$$

Combine 6y and -\frac{4}{5}y to get \frac{26}{5}y.

$$\frac{2}{7}y^{3}-y^{2}+\frac{26}{5}y-\frac{3}{7}+\frac{1}{7}$$

Add -\frac{3}{7} and \frac{1}{7} to get -\frac{2}{7}.

$$\frac{2}{7}y^{3}-y^{2}+\frac{26}{5}y-\frac{2}{7}$$