Solve 9x^3 - 576x^6

Question

Factor the expression

9 x^{3} (1 - 4 x) (1 + 4 x + 16 x^{2})

Evaluate

9 x^{3} - 576 x^{6}

Factor out 9 x^{3} from the expression

9 x^{3} (1 - 64 x^{3})

Solution

More Steps

Evaluate

1 - 64 x^{3}

Rewrite the expression in exponential form

1^{3} - (4 x)^{3}

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

(1 - 4 x) (1^{2} + 1 \times 4 x + (4 x)^{2})

1 raised to any power equals to 1

(1 - 4 x) (1 + 1 \times 4 x + (4 x)^{2})

Any expression multiplied by 1 remains the same

(1 - 4 x) (1 + 4 x + (4 x)^{2})

Evaluate

More Steps

Evaluate

(4 x)^{2}

To raise a product to a power,raise each factor to that power

4^{2} x^{2}

Evaluate the power

16 x^{2}

(1 - 4 x) (1 + 4 x + 16 x^{2})

9 x^{3} (1 - 4 x) (1 + 4 x + 16 x^{2})

Show Solution

x_{1} = 0, x_{2} = \frac{1}{4}

Alternative Form

x_{1} = 0, x_{2} = 0.25

Evaluate

9 x^{3} - 576 x^{6}

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

9 x^{3} - 576 x^{6} = 0

Factor the expression

9 x^{3} (1 - 64 x^{3}) = 0

Divide both sides

x^{3} (1 - 64 x^{3}) = 0

Separate the equation into 2 possible cases

x^{3} = 0 1 - 64 x^{3} = 0

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

x = 0 1 - 64 x^{3} = 0

Solve the equation

More Steps

Evaluate

1 - 64 x^{3} = 0

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

- 64 x^{3} = 0 - 1

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

- 64 x^{3} = - 1

Change the signs on both sides of the equation

64 x^{3} = 1

Divide both sides

\frac{64 x ^{3}}{64} = \frac{1}{64}

Divide the numbers

x^{3} = \frac{1}{64}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{1}{64}

Calculate

x = 3 \frac{1}{64}

Simplify the root

More Steps

Evaluate

3 \frac{1}{64}

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

\frac{3 1}{3 64}

Simplify the radical expression

\frac{1}{3 64}

Simplify the radical expression

\frac{1}{4}

x = \frac{1}{4}

x = 0 x = \frac{1}{4}

Solution

x_{1} = 0, x_{2} = \frac{1}{4}

Alternative Form

x_{1} = 0, x_{2} = 0.25

Show Solution