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x^{4}-34x^{2}+225
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x^{4}-34x^{2}+225
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\left(x^{2}+5x+3x+15\right)\left(x-5\right)\left(x-3\right)
Apply the distributive property by multiplying each term of x+3 by each term of x+5.
\left(x^{2}+8x+15\right)\left(x-5\right)\left(x-3\right)
Combine 5x and 3x to get 8x.
\left(x^{3}-5x^{2}+8x^{2}-40x+15x-75\right)\left(x-3\right)
Apply the distributive property by multiplying each term of x^{2}+8x+15 by each term of x-5.
\left(x^{3}+3x^{2}-40x+15x-75\right)\left(x-3\right)
Combine -5x^{2} and 8x^{2} to get 3x^{2}.
\left(x^{3}+3x^{2}-25x-75\right)\left(x-3\right)
Combine -40x and 15x to get -25x.
x^{4}-3x^{3}+3x^{3}-9x^{2}-25x^{2}+75x-75x+225
Apply the distributive property by multiplying each term of x^{3}+3x^{2}-25x-75 by each term of x-3.
x^{4}-9x^{2}-25x^{2}+75x-75x+225
Combine -3x^{3} and 3x^{3} to get 0.
x^{4}-34x^{2}+75x-75x+225
Combine -9x^{2} and -25x^{2} to get -34x^{2}.
x^{4}-34x^{2}+225
Combine 75x and -75x to get 0.
\left(x^{2}+5x+3x+15\right)\left(x-5\right)\left(x-3\right)
Apply the distributive property by multiplying each term of x+3 by each term of x+5.
\left(x^{2}+8x+15\right)\left(x-5\right)\left(x-3\right)
Combine 5x and 3x to get 8x.
\left(x^{3}-5x^{2}+8x^{2}-40x+15x-75\right)\left(x-3\right)
Apply the distributive property by multiplying each term of x^{2}+8x+15 by each term of x-5.
\left(x^{3}+3x^{2}-40x+15x-75\right)\left(x-3\right)
Combine -5x^{2} and 8x^{2} to get 3x^{2}.
\left(x^{3}+3x^{2}-25x-75\right)\left(x-3\right)
Combine -40x and 15x to get -25x.
x^{4}-3x^{3}+3x^{3}-9x^{2}-25x^{2}+75x-75x+225
Apply the distributive property by multiplying each term of x^{3}+3x^{2}-25x-75 by each term of x-3.
x^{4}-9x^{2}-25x^{2}+75x-75x+225
Combine -3x^{3} and 3x^{3} to get 0.
x^{4}-34x^{2}+75x-75x+225
Combine -9x^{2} and -25x^{2} to get -34x^{2}.
x^{4}-34x^{2}+225
Combine 75x and -75x to get 0.
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
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\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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