Evaluate
-\left(2b-3c\right)^{2}+a^{2}
Expand
a^{2}-4b^{2}+12bc-9c^{2}
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a^{2}-2ab+3ac+2ba-4b^{2}+6bc-3ca+6bc-9c^{2}
Apply the distributive property by multiplying each term of a+2b-3c by each term of a-2b+3c.
a^{2}+3ac-4b^{2}+6bc-3ca+6bc-9c^{2}
Combine -2ab and 2ba to get 0.
a^{2}-4b^{2}+6bc+6bc-9c^{2}
Combine 3ac and -3ca to get 0.
a^{2}-4b^{2}+12bc-9c^{2}
Combine 6bc and 6bc to get 12bc.
a^{2}-2ab+3ac+2ba-4b^{2}+6bc-3ca+6bc-9c^{2}
Apply the distributive property by multiplying each term of a+2b-3c by each term of a-2b+3c.
a^{2}+3ac-4b^{2}+6bc-3ca+6bc-9c^{2}
Combine -2ab and 2ba to get 0.
a^{2}-4b^{2}+6bc+6bc-9c^{2}
Combine 3ac and -3ca to get 0.
a^{2}-4b^{2}+12bc-9c^{2}
Combine 6bc and 6bc to get 12bc.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
Arithmetic
699 * 533
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}