( - a ^ { 2 } b + 2 a b - b ^ { 2 } ) \div b + ( a + b ) ( a - b
Evaluate
2a-b^{2}-b
Expand
2a-b^{2}-b
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\frac{b\left(-a^{2}+2a-b\right)}{b}+\left(a+b\right)\left(a-b\right)
Factor the expressions that are not already factored in \frac{\left(-a^{2}\right)b+2ab-b^{2}}{b}.
-a^{2}+2a-b+\left(a+b\right)\left(a-b\right)
Cancel out b in both numerator and denominator.
-a^{2}+2a-b+a^{2}-b^{2}
Consider \left(a+b\right)\left(a-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}.
2a-b-b^{2}
Combine -a^{2} and a^{2} to get 0.
\frac{b\left(-a^{2}+2a-b\right)}{b}+\left(a+b\right)\left(a-b\right)
Factor the expressions that are not already factored in \frac{\left(-a^{2}\right)b+2ab-b^{2}}{b}.
-a^{2}+2a-b+\left(a+b\right)\left(a-b\right)
Cancel out b in both numerator and denominator.
-a^{2}+2a-b+a^{2}-b^{2}
Consider \left(a+b\right)\left(a-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}.
2a-b-b^{2}
Combine -a^{2} and a^{2} to get 0.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}