Evaluate
\left(3x-2y\right)\left(x+4y\right)
Expand
3x^{2}+10xy-8y^{2}
Share
Copied to clipboard
4x^{2}+4xy+y^{2}-\left(3y-x\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+y\right)^{2}.
4x^{2}+4xy+y^{2}-\left(9y^{2}-6yx+x^{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3y-x\right)^{2}.
4x^{2}+4xy+y^{2}-9y^{2}+6yx-x^{2}
To find the opposite of 9y^{2}-6yx+x^{2}, find the opposite of each term.
4x^{2}+4xy-8y^{2}+6yx-x^{2}
Combine y^{2} and -9y^{2} to get -8y^{2}.
4x^{2}+10xy-8y^{2}-x^{2}
Combine 4xy and 6yx to get 10xy.
3x^{2}+10xy-8y^{2}
Combine 4x^{2} and -x^{2} to get 3x^{2}.
4x^{2}+4xy+y^{2}-\left(3y-x\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+y\right)^{2}.
4x^{2}+4xy+y^{2}-\left(9y^{2}-6yx+x^{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3y-x\right)^{2}.
4x^{2}+4xy+y^{2}-9y^{2}+6yx-x^{2}
To find the opposite of 9y^{2}-6yx+x^{2}, find the opposite of each term.
4x^{2}+4xy-8y^{2}+6yx-x^{2}
Combine y^{2} and -9y^{2} to get -8y^{2}.
4x^{2}+10xy-8y^{2}-x^{2}
Combine 4xy and 6yx to get 10xy.
3x^{2}+10xy-8y^{2}
Combine 4x^{2} and -x^{2} to get 3x^{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}