Solve [12xy-(-7xy+13xy)-5xy]^2:(-3x^2)-(-2y)^2

$$[ 12 x y - ( - 7 x y + 13 x y ) - 5 x y ] ^ { 2 } : ( - 3 x ^ { 2 } ) - ( - 2 y ) ^ { 2 }$$

Evaluate

$$-\frac{13y^{2}}{3}$$

Solution Steps

Combine -7xy and 13xy to get 6xy.

$$\frac{\left(12xy-6xy-5xy\right)^{2}}{-3x^{2}}-\left(-2y\right)^{2}$$

Combine 12xy and -6xy to get 6xy.

$$\frac{\left(6xy-5xy\right)^{2}}{-3x^{2}}-\left(-2y\right)^{2}$$

Combine 6xy and -5xy to get xy.

$$\frac{\left(xy\right)^{2}}{-3x^{2}}-\left(-2y\right)^{2}$$

Expand \left(xy\right)^{2}.

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

Cancel out x^{2} in both numerator and denominator.

$$\frac{y^{2}}{-3}-\left(-2y\right)^{2}$$

Expand \left(-2y\right)^{2}.

$$\frac{y^{2}}{-3}-\left(-2\right)^{2}y^{2}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{y^{2}}{-3}-4y^{2}$$

Combine \frac{y^{2}}{-3} and -4y^{2} to get -\frac{13}{3}y^{2}.

$$-\frac{13}{3}y^{2}$$

Expand

$$-\frac{13y^{2}}{3}$$

Solution Steps

Combine -7xy and 13xy to get 6xy.

$$\frac{\left(12xy-6xy-5xy\right)^{2}}{-3x^{2}}-\left(-2y\right)^{2}$$

Combine 12xy and -6xy to get 6xy.

$$\frac{\left(6xy-5xy\right)^{2}}{-3x^{2}}-\left(-2y\right)^{2}$$

Combine 6xy and -5xy to get xy.

$$\frac{\left(xy\right)^{2}}{-3x^{2}}-\left(-2y\right)^{2}$$

Expand \left(xy\right)^{2}.

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

Cancel out x^{2} in both numerator and denominator.

$$\frac{y^{2}}{-3}-\left(-2y\right)^{2}$$

Expand \left(-2y\right)^{2}.

$$\frac{y^{2}}{-3}-\left(-2\right)^{2}y^{2}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{y^{2}}{-3}-4y^{2}$$

Combine \frac{y^{2}}{-3} and -4y^{2} to get -\frac{13}{3}y^{2}.

$$-\frac{13}{3}y^{2}$$