Solve (6x-y)^2-(6x+y)^2=48

$$( 6 x - y ) ^ { 2 } - ( 6 x + y ) ^ { 2 } = 48$$

Solve for x

$$x=-\frac{2}{y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6x-y\right)^{2}.

$$36x^{2}-12xy+y^{2}-\left(6x+y\right)^{2}=48$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(6x+y\right)^{2}.

$$36x^{2}-12xy+y^{2}-\left(36x^{2}+12xy+y^{2}\right)=48$$

To find the opposite of 36x^{2}+12xy+y^{2}, find the opposite of each term.

$$36x^{2}-12xy+y^{2}-36x^{2}-12xy-y^{2}=48$$

Combine 36x^{2} and -36x^{2} to get 0.

$$-12xy+y^{2}-12xy-y^{2}=48$$

Combine -12xy and -12xy to get -24xy.

$$-24xy+y^{2}-y^{2}=48$$

Combine y^{2} and -y^{2} to get 0.

$$-24xy=48$$

The equation is in standard form.

$$\left(-24y\right)x=48$$

Divide both sides by -24y.

$$\frac{\left(-24y\right)x}{-24y}=\frac{48}{-24y}$$

Dividing by -24y undoes the multiplication by -24y.

$$x=\frac{48}{-24y}$$

Divide 48 by -24y.

$$x=-\frac{2}{y}$$

Solve for y

$$y=-\frac{2}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6x-y\right)^{2}.

$$36x^{2}-12xy+y^{2}-\left(6x+y\right)^{2}=48$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(6x+y\right)^{2}.

$$36x^{2}-12xy+y^{2}-\left(36x^{2}+12xy+y^{2}\right)=48$$

To find the opposite of 36x^{2}+12xy+y^{2}, find the opposite of each term.

$$36x^{2}-12xy+y^{2}-36x^{2}-12xy-y^{2}=48$$

Combine 36x^{2} and -36x^{2} to get 0.

$$-12xy+y^{2}-12xy-y^{2}=48$$

Combine -12xy and -12xy to get -24xy.

$$-24xy+y^{2}-y^{2}=48$$

Combine y^{2} and -y^{2} to get 0.

$$-24xy=48$$

The equation is in standard form.

$$\left(-24x\right)y=48$$

Divide both sides by -24x.

$$\frac{\left(-24x\right)y}{-24x}=\frac{48}{-24x}$$

Dividing by -24x undoes the multiplication by -24x.

$$y=\frac{48}{-24x}$$

Divide 48 by -24x.

$$y=-\frac{2}{x}$$