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