Evaluate
x\left(3x+4y\right)
Expand
3x^{2}+4xy
Quiz
Algebra
5 problems similar to:
( 2 x + y ) ( 2 x - y ) + ( x + y ) ^ { 2 } - 2 ( x ^ { 2 } - x y )
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\left(2x\right)^{2}-y^{2}+\left(x+y\right)^{2}-2\left(x^{2}-xy\right)
Consider \left(2x+y\right)\left(2x-y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
2^{2}x^{2}-y^{2}+\left(x+y\right)^{2}-2\left(x^{2}-xy\right)
Expand \left(2x\right)^{2}.
4x^{2}-y^{2}+\left(x+y\right)^{2}-2\left(x^{2}-xy\right)
Calculate 2 to the power of 2 and get 4.
4x^{2}-y^{2}+x^{2}+2xy+y^{2}-2\left(x^{2}-xy\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+y\right)^{2}.
5x^{2}-y^{2}+2xy+y^{2}-2\left(x^{2}-xy\right)
Combine 4x^{2} and x^{2} to get 5x^{2}.
5x^{2}+2xy-2\left(x^{2}-xy\right)
Combine -y^{2} and y^{2} to get 0.
5x^{2}+2xy-2x^{2}+2xy
Use the distributive property to multiply -2 by x^{2}-xy.
3x^{2}+2xy+2xy
Combine 5x^{2} and -2x^{2} to get 3x^{2}.
3x^{2}+4xy
Combine 2xy and 2xy to get 4xy.
\left(2x\right)^{2}-y^{2}+\left(x+y\right)^{2}-2\left(x^{2}-xy\right)
Consider \left(2x+y\right)\left(2x-y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
2^{2}x^{2}-y^{2}+\left(x+y\right)^{2}-2\left(x^{2}-xy\right)
Expand \left(2x\right)^{2}.
4x^{2}-y^{2}+\left(x+y\right)^{2}-2\left(x^{2}-xy\right)
Calculate 2 to the power of 2 and get 4.
4x^{2}-y^{2}+x^{2}+2xy+y^{2}-2\left(x^{2}-xy\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+y\right)^{2}.
5x^{2}-y^{2}+2xy+y^{2}-2\left(x^{2}-xy\right)
Combine 4x^{2} and x^{2} to get 5x^{2}.
5x^{2}+2xy-2\left(x^{2}-xy\right)
Combine -y^{2} and y^{2} to get 0.
5x^{2}+2xy-2x^{2}+2xy
Use the distributive property to multiply -2 by x^{2}-xy.
3x^{2}+2xy+2xy
Combine 5x^{2} and -2x^{2} to get 3x^{2}.
3x^{2}+4xy
Combine 2xy and 2xy to get 4xy.
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}