Solve (2x^3-3x)^5

Question

Simplify the expression

32 x^{15} - 240 x^{13} + 720 x^{11} - 1080 x^{9} + 810 x^{7} - 243 x^{5}

Evaluate

(2 x^{3} - 3 x)^{5}

Solution

32 x^{15} - 240 x^{13} + 720 x^{11} - 1080 x^{9} + 810 x^{7} - 243 x^{5}

Show Solution

x^{5} (2 x^{2} - 3)^{5}

Evaluate

(2 x^{3} - 3 x)^{5}

Factor the expression

More Steps

Evaluate

2 x^{3} - 3 x

Rewrite the expression

x \times 2 x^{2} - x \times 3

Factor out x from the expression

x (2 x^{2} - 3)

(x (2 x^{2} - 3))^{5}

Solution

x^{5} (2 x^{2} - 3)^{5}

Show Solution

x_{1} = - \frac{6}{2}, x_{2} = 0, x_{3} = \frac{6}{2}

Alternative Form

x_{1} \approx - 1.224745, x_{2} = 0, x_{3} \approx 1.224745

Evaluate

(2 x^{3} - 3 x)^{5}

To find the roots of the expression,set the expression equal to 0

(2 x^{3} - 3 x)^{5} = 0

The only way a power can be 0 is when the base equals 0

2 x^{3} - 3 x = 0

Factor the expression

x (2 x^{2} - 3) = 0

Separate the equation into 2 possible cases

x = 0 2 x^{2} - 3 = 0

Solve the equation

More Steps

Evaluate

2 x^{2} - 3 = 0

Move the constant to the right-hand side and change its sign

2 x^{2} = 0 + 3

Removing 0 doesn't change the value,so remove it from the expression

2 x^{2} = 3

Divide both sides

\frac{2 x ^{2}}{2} = \frac{3}{2}

Divide the numbers

x^{2} = \frac{3}{2}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{3}{2}

Simplify the expression

More Steps

Evaluate

\frac{3}{2}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3}{2}

Multiply by the Conjugate

\frac{3 \times 2}{2 \times 2}

Multiply the numbers

\frac{6}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{6}{2}

x = \pm \frac{6}{2}

Separate the equation into 2 possible cases

x = \frac{6}{2} x = - \frac{6}{2}

x = 0 x = \frac{6}{2} x = - \frac{6}{2}

Solution

x_{1} = - \frac{6}{2}, x_{2} = 0, x_{3} = \frac{6}{2}

Alternative Form

x_{1} \approx - 1.224745, x_{2} = 0, x_{3} \approx 1.224745

Show Solution