Solve 25x^5:(-5x^2)+3x^3-(-30ax^3):(5a)+2x(-4

$$25 x ^ { 5 } : ( - 5 x ^ { 2 } ) + 3 x ^ { 3 } - ( - 30 a x ^ { 3 } ) : ( 5 a ) + 2 x ( - 4$$

Evaluate

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

Solution Steps

Cancel out 5x^{2} in both numerator and denominator.

$$\frac{5x^{3}}{-1}+3x^{3}-\frac{-30ax^{3}}{5a}+2x\left(-4\right)$$

Anything divided by -1 gives its opposite.

$$-5x^{3}+3x^{3}-\frac{-30ax^{3}}{5a}+2x\left(-4\right)$$

Combine -5x^{3} and 3x^{3} to get -2x^{3}.

$$-2x^{3}-\frac{-30ax^{3}}{5a}+2x\left(-4\right)$$

Cancel out 5a in both numerator and denominator.

$$-2x^{3}-\left(-6x^{3}\right)+2x\left(-4\right)$$

The opposite of -6x^{3} is 6x^{3}.

$$-2x^{3}+6x^{3}+2x\left(-4\right)$$

Combine -2x^{3} and 6x^{3} to get 4x^{3}.

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

Multiply 2 and -4 to get -8.

$$4x^{3}-8x$$

Factor

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

Solution Steps

Cancel out 5x^{2} in both numerator and denominator.

$$factor(\frac{5x^{3}}{-1}+3x^{3}-\frac{-30ax^{3}}{5a}+2x\left(-4\right))$$

Anything divided by -1 gives its opposite.

$$factor(-5x^{3}+3x^{3}-\frac{-30ax^{3}}{5a}+2x\left(-4\right))$$

Combine -5x^{3} and 3x^{3} to get -2x^{3}.

$$factor(-2x^{3}-\frac{-30ax^{3}}{5a}+2x\left(-4\right))$$

Cancel out 5a in both numerator and denominator.

$$factor(-2x^{3}-\left(-6x^{3}\right)+2x\left(-4\right))$$

The opposite of -6x^{3} is 6x^{3}.

$$factor(-2x^{3}+6x^{3}+2x\left(-4\right))$$

Combine -2x^{3} and 6x^{3} to get 4x^{3}.

$$factor(4x^{3}+2x\left(-4\right))$$

Multiply 2 and -4 to get -8.

$$factor(4x^{3}-8x)$$

Factor out 4.

$$4\left(x^{3}-2x\right)$$

Consider x^{3}-2x. Factor out x.

$$x\left(x^{2}-2\right)$$

Rewrite the complete factored expression. Polynomial x^{2}-2 is not factored since it does not have any rational roots.

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