Solve left(3xy+7right)^2-left(3xy-7right)^2=8xy

$${ \left(3xy+7 \right) }^{ 2 } - { \left(3xy-7 \right) }^{ 2 } = 8xy$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3xy+7\right)^{2}.

$$9x^{2}y^{2}+42xy+49-\left(3xy-7\right)^{2}=8xy$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3xy-7\right)^{2}.

$$9x^{2}y^{2}+42xy+49-\left(9x^{2}y^{2}-42xy+49\right)=8xy$$

To find the opposite of 9x^{2}y^{2}-42xy+49, find the opposite of each term.

$$9x^{2}y^{2}+42xy+49-9x^{2}y^{2}+42xy-49=8xy$$

Combine 9x^{2}y^{2} and -9x^{2}y^{2} to get 0.

$$42xy+49+42xy-49=8xy$$

Combine 42xy and 42xy to get 84xy.

$$84xy+49-49=8xy$$

Subtract 49 from 49 to get 0.

$$84xy=8xy$$

Subtract 8xy from both sides.

$$84xy-8xy=0$$

Combine 84xy and -8xy to get 76xy.

$$76xy=0$$

The equation is in standard form.

$$76yx=0$$

Divide 0 by 76y.

$$x=0$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3xy+7\right)^{2}.

$$9x^{2}y^{2}+42xy+49-\left(3xy-7\right)^{2}=8xy$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3xy-7\right)^{2}.

$$9x^{2}y^{2}+42xy+49-\left(9x^{2}y^{2}-42xy+49\right)=8xy$$

To find the opposite of 9x^{2}y^{2}-42xy+49, find the opposite of each term.

$$9x^{2}y^{2}+42xy+49-9x^{2}y^{2}+42xy-49=8xy$$

Combine 9x^{2}y^{2} and -9x^{2}y^{2} to get 0.

$$42xy+49+42xy-49=8xy$$

Combine 42xy and 42xy to get 84xy.

$$84xy+49-49=8xy$$

Subtract 49 from 49 to get 0.

$$84xy=8xy$$

Subtract 8xy from both sides.

$$84xy-8xy=0$$

Combine 84xy and -8xy to get 76xy.

$$76xy=0$$

Divide 0 by 76x.

$$y=0$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3xy+7\right)^{2}.

$$9x^{2}y^{2}+42xy+49-\left(3xy-7\right)^{2}=8xy$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3xy-7\right)^{2}.

$$9x^{2}y^{2}+42xy+49-\left(9x^{2}y^{2}-42xy+49\right)=8xy$$

To find the opposite of 9x^{2}y^{2}-42xy+49, find the opposite of each term.

$$9x^{2}y^{2}+42xy+49-9x^{2}y^{2}+42xy-49=8xy$$

Combine 9x^{2}y^{2} and -9x^{2}y^{2} to get 0.

$$42xy+49+42xy-49=8xy$$

Combine 42xy and 42xy to get 84xy.

$$84xy+49-49=8xy$$

Subtract 49 from 49 to get 0.

$$84xy=8xy$$

Subtract 8xy from both sides.

$$84xy-8xy=0$$

Combine 84xy and -8xy to get 76xy.

$$76xy=0$$

The equation is in standard form.

$$76yx=0$$

Divide 0 by 76y.

$$x=0$$

Solve for y

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3xy+7\right)^{2}.

$$9x^{2}y^{2}+42xy+49-\left(3xy-7\right)^{2}=8xy$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3xy-7\right)^{2}.

$$9x^{2}y^{2}+42xy+49-\left(9x^{2}y^{2}-42xy+49\right)=8xy$$

To find the opposite of 9x^{2}y^{2}-42xy+49, find the opposite of each term.

$$9x^{2}y^{2}+42xy+49-9x^{2}y^{2}+42xy-49=8xy$$

Combine 9x^{2}y^{2} and -9x^{2}y^{2} to get 0.

$$42xy+49+42xy-49=8xy$$

Combine 42xy and 42xy to get 84xy.

$$84xy+49-49=8xy$$

Subtract 49 from 49 to get 0.

$$84xy=8xy$$

Subtract 8xy from both sides.

$$84xy-8xy=0$$

Combine 84xy and -8xy to get 76xy.

$$76xy=0$$

Divide 0 by 76x.

$$y=0$$