Solve (x^{2}y-1/7x^{2}y)(-3y^{2}+1/12y^{2})(2/5x^{2}y^{2}+2x^2y^2)-3x^4y^5

$$( x ^ { 2 } y - \frac { 1 } { 7 } x ^ { 2 } y ) ( - 3 y ^ { 2 } + \frac { 1 } { 12 } y ^ { 2 } ) ( \frac { 2 } { 5 } x ^ { 2 } y ^ { 2 } + 2 x ^ { 2 } y ^ { 2 } ) - 3 x ^ { 4 } y ^ { 5 }$$

Evaluate

$$-9x^{4}y^{5}$$

Solution Steps

Combine x^{2}y and -\frac{1}{7}x^{2}y to get \frac{6}{7}x^{2}y.

$$\frac{6}{7}x^{2}y\left(-3y^{2}+\frac{1}{12}y^{2}\right)\left(\frac{2}{5}x^{2}y^{2}+2x^{2}y^{2}\right)-3x^{4}y^{5}$$

Combine -3y^{2} and \frac{1}{12}y^{2} to get -\frac{35}{12}y^{2}.

$$\frac{6}{7}x^{2}y\left(-\frac{35}{12}\right)y^{2}\left(\frac{2}{5}x^{2}y^{2}+2x^{2}y^{2}\right)-3x^{4}y^{5}$$

Multiply \frac{6}{7} and -\frac{35}{12} to get -\frac{5}{2}.

$$-\frac{5}{2}x^{2}yy^{2}\left(\frac{2}{5}x^{2}y^{2}+2x^{2}y^{2}\right)-3x^{4}y^{5}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-\frac{5}{2}x^{2}y^{3}\left(\frac{2}{5}x^{2}y^{2}+2x^{2}y^{2}\right)-3x^{4}y^{5}$$

Combine \frac{2}{5}x^{2}y^{2} and 2x^{2}y^{2} to get \frac{12}{5}x^{2}y^{2}.

$$-\frac{5}{2}x^{2}y^{3}\times \frac{12}{5}x^{2}y^{2}-3x^{4}y^{5}$$

Multiply -\frac{5}{2} and \frac{12}{5} to get -6.

$$-6x^{2}y^{3}x^{2}y^{2}-3x^{4}y^{5}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$-6x^{4}y^{3}y^{2}-3x^{4}y^{5}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-6x^{4}y^{5}-3x^{4}y^{5}$$

Combine -6x^{4}y^{5} and -3x^{4}y^{5} to get -9x^{4}y^{5}.

$$-9x^{4}y^{5}$$

Expand

$$-9x^{4}y^{5}$$

Solution Steps

Combine x^{2}y and -\frac{1}{7}x^{2}y to get \frac{6}{7}x^{2}y.

$$\frac{6}{7}x^{2}y\left(-3y^{2}+\frac{1}{12}y^{2}\right)\left(\frac{2}{5}x^{2}y^{2}+2x^{2}y^{2}\right)-3x^{4}y^{5}$$

Combine -3y^{2} and \frac{1}{12}y^{2} to get -\frac{35}{12}y^{2}.

$$\frac{6}{7}x^{2}y\left(-\frac{35}{12}\right)y^{2}\left(\frac{2}{5}x^{2}y^{2}+2x^{2}y^{2}\right)-3x^{4}y^{5}$$

Multiply \frac{6}{7} and -\frac{35}{12} to get -\frac{5}{2}.

$$-\frac{5}{2}x^{2}yy^{2}\left(\frac{2}{5}x^{2}y^{2}+2x^{2}y^{2}\right)-3x^{4}y^{5}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-\frac{5}{2}x^{2}y^{3}\left(\frac{2}{5}x^{2}y^{2}+2x^{2}y^{2}\right)-3x^{4}y^{5}$$

Combine \frac{2}{5}x^{2}y^{2} and 2x^{2}y^{2} to get \frac{12}{5}x^{2}y^{2}.

$$-\frac{5}{2}x^{2}y^{3}\times \frac{12}{5}x^{2}y^{2}-3x^{4}y^{5}$$

Multiply -\frac{5}{2} and \frac{12}{5} to get -6.

$$-6x^{2}y^{3}x^{2}y^{2}-3x^{4}y^{5}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$-6x^{4}y^{3}y^{2}-3x^{4}y^{5}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-6x^{4}y^{5}-3x^{4}y^{5}$$

Combine -6x^{4}y^{5} and -3x^{4}y^{5} to get -9x^{4}y^{5}.

$$-9x^{4}y^{5}$$