Evaluate
\left(2x+y\right)^{2}+\left(3x-2y\right)^{2}
Expand
13x^{2}-8xy+5y^{2}
Share
Copied to clipboard
9x^{2}-12xy+4y^{2}+\left(2x+y\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-2y\right)^{2}.
9x^{2}-12xy+4y^{2}+4x^{2}+4xy+y^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+y\right)^{2}.
13x^{2}-12xy+4y^{2}+4xy+y^{2}
Combine 9x^{2} and 4x^{2} to get 13x^{2}.
13x^{2}-8xy+4y^{2}+y^{2}
Combine -12xy and 4xy to get -8xy.
13x^{2}-8xy+5y^{2}
Combine 4y^{2} and y^{2} to get 5y^{2}.
9x^{2}-12xy+4y^{2}+\left(2x+y\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-2y\right)^{2}.
9x^{2}-12xy+4y^{2}+4x^{2}+4xy+y^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+y\right)^{2}.
13x^{2}-12xy+4y^{2}+4xy+y^{2}
Combine 9x^{2} and 4x^{2} to get 13x^{2}.
13x^{2}-8xy+4y^{2}+y^{2}
Combine -12xy and 4xy to get -8xy.
13x^{2}-8xy+5y^{2}
Combine 4y^{2} and y^{2} to get 5y^{2}.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}