Evaluate
\frac{\left(x-1\right)\left(x+7\right)}{4}
Expand
\frac{x^{2}}{4}+\frac{3x}{2}-\frac{7}{4}
Graph
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\left(\frac{1}{4}x+\frac{1}{4}\left(-1\right)\right)\left(x+7\right)
Use the distributive property to multiply \frac{1}{4} by x-1.
\left(\frac{1}{4}x-\frac{1}{4}\right)\left(x+7\right)
Multiply \frac{1}{4} and -1 to get -\frac{1}{4}.
\frac{1}{4}xx+\frac{1}{4}x\times 7-\frac{1}{4}x-\frac{1}{4}\times 7
Apply the distributive property by multiplying each term of \frac{1}{4}x-\frac{1}{4} by each term of x+7.
\frac{1}{4}x^{2}+\frac{1}{4}x\times 7-\frac{1}{4}x-\frac{1}{4}\times 7
Multiply x and x to get x^{2}.
\frac{1}{4}x^{2}+\frac{7}{4}x-\frac{1}{4}x-\frac{1}{4}\times 7
Multiply \frac{1}{4} and 7 to get \frac{7}{4}.
\frac{1}{4}x^{2}+\frac{3}{2}x-\frac{1}{4}\times 7
Combine \frac{7}{4}x and -\frac{1}{4}x to get \frac{3}{2}x.
\frac{1}{4}x^{2}+\frac{3}{2}x+\frac{-7}{4}
Express -\frac{1}{4}\times 7 as a single fraction.
\frac{1}{4}x^{2}+\frac{3}{2}x-\frac{7}{4}
Fraction \frac{-7}{4} can be rewritten as -\frac{7}{4} by extracting the negative sign.
\left(\frac{1}{4}x+\frac{1}{4}\left(-1\right)\right)\left(x+7\right)
Use the distributive property to multiply \frac{1}{4} by x-1.
\left(\frac{1}{4}x-\frac{1}{4}\right)\left(x+7\right)
Multiply \frac{1}{4} and -1 to get -\frac{1}{4}.
\frac{1}{4}xx+\frac{1}{4}x\times 7-\frac{1}{4}x-\frac{1}{4}\times 7
Apply the distributive property by multiplying each term of \frac{1}{4}x-\frac{1}{4} by each term of x+7.
\frac{1}{4}x^{2}+\frac{1}{4}x\times 7-\frac{1}{4}x-\frac{1}{4}\times 7
Multiply x and x to get x^{2}.
\frac{1}{4}x^{2}+\frac{7}{4}x-\frac{1}{4}x-\frac{1}{4}\times 7
Multiply \frac{1}{4} and 7 to get \frac{7}{4}.
\frac{1}{4}x^{2}+\frac{3}{2}x-\frac{1}{4}\times 7
Combine \frac{7}{4}x and -\frac{1}{4}x to get \frac{3}{2}x.
\frac{1}{4}x^{2}+\frac{3}{2}x+\frac{-7}{4}
Express -\frac{1}{4}\times 7 as a single fraction.
\frac{1}{4}x^{2}+\frac{3}{2}x-\frac{7}{4}
Fraction \frac{-7}{4} can be rewritten as -\frac{7}{4} by extracting the negative sign.
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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