Evaluate
\left(x-2y+1\right)\left(x+2y+3\right)
Expand
x^{2}+4x-4y^{2}-4y+3
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x^{2}+4x+4-\left(2y+1\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.
x^{2}+4x+4-\left(4y^{2}+4y+1\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2y+1\right)^{2}.
x^{2}+4x+4-4y^{2}-4y-1
To find the opposite of 4y^{2}+4y+1, find the opposite of each term.
x^{2}+4x+3-4y^{2}-4y
Subtract 1 from 4 to get 3.
x^{2}+4x+4-\left(2y+1\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.
x^{2}+4x+4-\left(4y^{2}+4y+1\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2y+1\right)^{2}.
x^{2}+4x+4-4y^{2}-4y-1
To find the opposite of 4y^{2}+4y+1, find the opposite of each term.
x^{2}+4x+3-4y^{2}-4y
Subtract 1 from 4 to get 3.
Examples
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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
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