Type a math problem

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Type a math problem

Evaluate

-x\left(x-3\right)\left(x+1\right)

$−x(x−3)(x+1)$

Solution Steps

- 5 x - x ( x + 2 ) ( x - 4 )

$−5x−x(x+2)(x−4)$

Use the distributive property to multiply x by x+2.

Use the distributive property to multiply $x$ by $x+2$.

-5x-\left(x^{2}+2x\right)\left(x-4\right)

$−5x−(x_{2}+2x)(x−4)$

Apply the distributive property by multiplying each term of x^{2}+2x by each term of x-4.

Apply the distributive property by multiplying each term of $x_{2}+2x$ by each term of $x−4$.

-5x-\left(x^{3}-4x^{2}+2x^{2}-8x\right)

$−5x−(x_{3}−4x_{2}+2x_{2}−8x)$

Combine -4x^{2} and 2x^{2} to get -2x^{2}.

Combine $−4x_{2}$ and $2x_{2}$ to get $−2x_{2}$.

-5x-\left(x^{3}-2x^{2}-8x\right)

$−5x−(x_{3}−2x_{2}−8x)$

To find the opposite of x^{3}-2x^{2}-8x, find the opposite of each term.

To find the opposite of $x_{3}−2x_{2}−8x$, find the opposite of each term.

-5x-x^{3}-\left(-2x^{2}\right)-\left(-8x\right)

$−5x−x_{3}−(−2x_{2})−(−8x)$

The opposite of -2x^{2} is 2x^{2}.

The opposite of $−2x_{2}$ is $2x_{2}$.

-5x-x^{3}+2x^{2}-\left(-8x\right)

$−5x−x_{3}+2x_{2}−(−8x)$

The opposite of -8x is 8x.

The opposite of $−8x$ is $8x$.

-5x-x^{3}+2x^{2}+8x

$−5x−x_{3}+2x_{2}+8x$

Combine -5x and 8x to get 3x.

Combine $−5x$ and $8x$ to get $3x$.

3x-x^{3}+2x^{2}

$3x−x_{3}+2x_{2}$

Expand

3x+2x^{2}-x^{3}

$3x+2x_{2}−x_{3}$

Solution Steps

- 5 x - x ( x + 2 ) ( x - 4 )

$−5x−x(x+2)(x−4)$

Use the distributive property to multiply x by x+2.

Use the distributive property to multiply $x$ by $x+2$.

-5x-\left(x^{2}+2x\right)\left(x-4\right)

$−5x−(x_{2}+2x)(x−4)$

Apply the distributive property by multiplying each term of x^{2}+2x by each term of x-4.

Apply the distributive property by multiplying each term of $x_{2}+2x$ by each term of $x−4$.

-5x-\left(x^{3}-4x^{2}+2x^{2}-8x\right)

$−5x−(x_{3}−4x_{2}+2x_{2}−8x)$

Combine -4x^{2} and 2x^{2} to get -2x^{2}.

Combine $−4x_{2}$ and $2x_{2}$ to get $−2x_{2}$.

-5x-\left(x^{3}-2x^{2}-8x\right)

$−5x−(x_{3}−2x_{2}−8x)$

To find the opposite of x^{3}-2x^{2}-8x, find the opposite of each term.

To find the opposite of $x_{3}−2x_{2}−8x$, find the opposite of each term.

-5x-x^{3}-\left(-2x^{2}\right)-\left(-8x\right)

$−5x−x_{3}−(−2x_{2})−(−8x)$

The opposite of -2x^{2} is 2x^{2}.

The opposite of $−2x_{2}$ is $2x_{2}$.

-5x-x^{3}+2x^{2}-\left(-8x\right)

$−5x−x_{3}+2x_{2}−(−8x)$

The opposite of -8x is 8x.

The opposite of $−8x$ is $8x$.

-5x-x^{3}+2x^{2}+8x

$−5x−x_{3}+2x_{2}+8x$

Combine -5x and 8x to get 3x.

Combine $−5x$ and $8x$ to get $3x$.

3x-x^{3}+2x^{2}

$3x−x_{3}+2x_{2}$

Factor

-x\left(x-3\right)\left(x+1\right)

$−x(x−3)(x+1)$

Solution Steps

- 5 x - x ( x + 2 ) ( x - 4 )

$−5x−x(x+2)(x−4)$

Factor out common term x by using distributive property.

Factor out common term $x$ by using distributive property.

x\left(-\left(x+2\right)\left(x-4\right)-5\right)

$x(−(x+2)(x−4)−5)$

Consider -\left(x+2\right)\left(x-4\right)-5. Simplify.

Consider $−(x+2)(x−4)−5$. Simplify.

-x^{2}+2x+3

$−x_{2}+2x+3$

Factor the expression by grouping. First, the expression needs to be rewritten as -x^{2}+ax+bx+3. To find a and b, set up a system to be solved.

Factor the expression by grouping. First, the expression needs to be rewritten as $−x_{2}+ax+bx+3$. To find $a$ and $b$, set up a system to be solved.

a+b=2 ab=-3=-3

$a+b=2$ $ab=−3=−3$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. The only such pair is the system solution.

Since $ab$ is negative, $a$ and $b$ have the opposite signs. Since $a+b$ is positive, the positive number has greater absolute value than the negative. The only such pair is the system solution.

a=3 b=-1

$a=3$ $b=−1$

Rewrite -x^{2}+2x+3 as \left(-x^{2}+3x\right)+\left(-x+3\right).

Rewrite $−x_{2}+2x+3$ as $(−x_{2}+3x)+(−x+3)$.

\left(-x^{2}+3x\right)+\left(-x+3\right)

$(−x_{2}+3x)+(−x+3)$

Factor out -x in the first and -1 in the second group.

Factor out $−x$ in the first and $−1$ in the second group.

-x\left(x-3\right)-\left(x-3\right)

$−x(x−3)−(x−3)$

Factor out common term x-3 by using distributive property.

Factor out common term $x−3$ by using distributive property.

\left(x-3\right)\left(-x-1\right)

$(x−3)(−x−1)$

Rewrite the complete factored expression.

Rewrite the complete factored expression.

x\left(x-3\right)\left(-x-1\right)

$x(x−3)(−x−1)$

Graph

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-5x-\left(x^{2}+2x\right)\left(x-4\right)

Use the distributive property to multiply x by x+2.

-5x-\left(x^{3}-4x^{2}+2x^{2}-8x\right)

Apply the distributive property by multiplying each term of x^{2}+2x by each term of x-4.

-5x-\left(x^{3}-2x^{2}-8x\right)

Combine -4x^{2} and 2x^{2} to get -2x^{2}.

-5x-x^{3}-\left(-2x^{2}\right)-\left(-8x\right)

To find the opposite of x^{3}-2x^{2}-8x, find the opposite of each term.

-5x-x^{3}+2x^{2}-\left(-8x\right)

The opposite of -2x^{2} is 2x^{2}.

-5x-x^{3}+2x^{2}+8x

The opposite of -8x is 8x.

3x-x^{3}+2x^{2}

Combine -5x and 8x to get 3x.

-5x-\left(x^{2}+2x\right)\left(x-4\right)

Use the distributive property to multiply x by x+2.

-5x-\left(x^{3}-4x^{2}+2x^{2}-8x\right)

Apply the distributive property by multiplying each term of x^{2}+2x by each term of x-4.

-5x-\left(x^{3}-2x^{2}-8x\right)

Combine -4x^{2} and 2x^{2} to get -2x^{2}.

-5x-x^{3}-\left(-2x^{2}\right)-\left(-8x\right)

To find the opposite of x^{3}-2x^{2}-8x, find the opposite of each term.

-5x-x^{3}+2x^{2}-\left(-8x\right)

The opposite of -2x^{2} is 2x^{2}.

-5x-x^{3}+2x^{2}+8x

The opposite of -8x is 8x.

3x-x^{3}+2x^{2}

Combine -5x and 8x to get 3x.

x\left(-\left(x+2\right)\left(x-4\right)-5\right)

Factor out common term x by using distributive property.

-x^{2}+2x+3

Consider -\left(x+2\right)\left(x-4\right)-5. Simplify.

a+b=2 ab=-3=-3

Factor the expression by grouping. First, the expression needs to be rewritten as -x^{2}+ax+bx+3. To find a and b, set up a system to be solved.

a=3 b=-1

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. The only such pair is the system solution.

\left(-x^{2}+3x\right)+\left(-x+3\right)

Rewrite -x^{2}+2x+3 as \left(-x^{2}+3x\right)+\left(-x+3\right).

-x\left(x-3\right)-\left(x-3\right)

Factor out -x in the first and -1 in the second group.

\left(x-3\right)\left(-x-1\right)

Factor out common term x-3 by using distributive property.

x\left(x-3\right)\left(-x-1\right)

Rewrite the complete factored expression.

Examples

Quadratic equation

{ x } ^ { 2 } - 4 x - 5 = 0

$x_{2}−4x−5=0$

Trigonometry

4 \sin \theta \cos \theta = 2 \sin \theta

$4sinθcosθ=2sinθ$

Linear equation

y = 3x + 4

$y=3x+4$

Arithmetic

699 * 533

$699∗533$

Matrix

\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { - 1 } & { 1 } & { 5 } \end{array} \right]

$[25 34 ][2−1 01 35 ]$

Simultaneous equation

\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.

${8x+2y=467x+3y=47 $

Differentiation

\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }

$dxd (x−5)(3x_{2}−2) $

Integration

\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x

$∫_{0}xe_{−x_{2}}dx$

Limits

\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}

$x→−3lim x_{2}+2x−3x_{2}−9 $

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