Evaluate
\left(x+6\right)^{2}-y^{2}
Expand
x^{2}+12x-y^{2}+36
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x^{2}+6x-xy+6x+36-6y+yx+6y-y^{2}
Apply the distributive property by multiplying each term of x+6+y by each term of x+6-y.
x^{2}+12x-xy+36-6y+yx+6y-y^{2}
Combine 6x and 6x to get 12x.
x^{2}+12x+36-6y+6y-y^{2}
Combine -xy and yx to get 0.
x^{2}+12x+36-y^{2}
Combine -6y and 6y to get 0.
x^{2}+6x-xy+6x+36-6y+yx+6y-y^{2}
Apply the distributive property by multiplying each term of x+6+y by each term of x+6-y.
x^{2}+12x-xy+36-6y+yx+6y-y^{2}
Combine 6x and 6x to get 12x.
x^{2}+12x+36-6y+6y-y^{2}
Combine -xy and yx to get 0.
x^{2}+12x+36-y^{2}
Combine -6y and 6y 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
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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}