Solve (x+y)^2-(x-y)^2=24

$$( x + y ) ^ { 2 } - ( x - y ) ^ { 2 } = 24$$

Solve for x

$$x=\frac{6}{y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

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

$$x^{2}+2xy+y^{2}-\left(x-y\right)^{2}=24$$

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

$$x^{2}+2xy+y^{2}-\left(x^{2}-2xy+y^{2}\right)=24$$

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

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

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

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

Combine 2xy and 2xy to get 4xy.

$$4xy+y^{2}-y^{2}=24$$

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

$$4xy=24$$

The equation is in standard form.

$$4yx=24$$

Divide both sides by 4y.

$$\frac{4yx}{4y}=\frac{24}{4y}$$

Dividing by 4y undoes the multiplication by 4y.

$$x=\frac{24}{4y}$$

Divide 24 by 4y.

$$x=\frac{6}{y}$$

Solve for y

$$y=\frac{6}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$x^{2}+2xy+y^{2}-\left(x-y\right)^{2}=24$$

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

$$x^{2}+2xy+y^{2}-\left(x^{2}-2xy+y^{2}\right)=24$$

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

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

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

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

Combine 2xy and 2xy to get 4xy.

$$4xy+y^{2}-y^{2}=24$$

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

$$4xy=24$$

Divide both sides by 4x.

$$\frac{4xy}{4x}=\frac{24}{4x}$$

Dividing by 4x undoes the multiplication by 4x.

$$y=\frac{24}{4x}$$

Divide 24 by 4x.

$$y=\frac{6}{x}$$