Evaluate
4a^{2}-a-b^{2}+b
Expand
4a^{2}-a-b^{2}+b
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\left(2a\right)^{2}-b^{2}-a+b
Consider \left(2a+b\right)\left(2a-b\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}a^{2}-b^{2}-a+b
Expand \left(2a\right)^{2}.
4a^{2}-b^{2}-a+b
Calculate 2 to the power of 2 and get 4.
\left(2a\right)^{2}-b^{2}-a+b
Consider \left(2a+b\right)\left(2a-b\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}a^{2}-b^{2}-a+b
Expand \left(2a\right)^{2}.
4a^{2}-b^{2}-a+b
Calculate 2 to the power of 2 and get 4.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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Matrix
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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}