Solve {l}{(x+3y)^2}{+(3x+y)^2}

$$\left. \begin{array} { l } { ( x + 3 y ) ^ { 2 } } \\ { + ( 3 x + y ) ^ { 2 } } \end{array} \right.$$

Evaluate

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

Solution Steps

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

$$x^{2}+6xy+9y^{2}+\left(3x+y\right)^{2}$$

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

$$x^{2}+6xy+9y^{2}+9x^{2}+6xy+y^{2}$$

Combine x^{2} and 9x^{2} to get 10x^{2}.

$$10x^{2}+6xy+9y^{2}+6xy+y^{2}$$

Combine 6xy and 6xy to get 12xy.

$$10x^{2}+12xy+9y^{2}+y^{2}$$

Combine 9y^{2} and y^{2} to get 10y^{2}.

$$10x^{2}+12xy+10y^{2}$$

Expand

$$10x^{2}+12xy+10y^{2}$$

Solution Steps

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

$$x^{2}+6xy+9y^{2}+\left(3x+y\right)^{2}$$

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

$$x^{2}+6xy+9y^{2}+9x^{2}+6xy+y^{2}$$

Combine x^{2} and 9x^{2} to get 10x^{2}.

$$10x^{2}+6xy+9y^{2}+6xy+y^{2}$$

Combine 6xy and 6xy to get 12xy.

$$10x^{2}+12xy+9y^{2}+y^{2}$$

Combine 9y^{2} and y^{2} to get 10y^{2}.

$$10x^{2}+12xy+10y^{2}$$