Solve 3x^3 3x^2-x ^3

Question

Simplify the expression

9 x^{5} - x^{3}

Evaluate

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

Solution

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

9 x^{3 + 2}

Add the numbers

9 x^{5}

9 x^{5} - x^{3}

Show Solution

Factor the expression

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

Evaluate

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

Evaluate

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

9 x^{3 + 2}

Add the numbers

9 x^{5}

9 x^{5} - x^{3}

Factor out x^{3} from the expression

x^{3} (9 x^{2} - 1)

Solution

More Steps

Evaluate

9 x^{2} - 1

Rewrite the expression in exponential form

(3 x)^{2} - 1^{2}

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

(3 x - 1) (3 x + 1)

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

Show Solution

Find the roots

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

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0, x_{3} = 0. \dot{3}

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

9 x^{3 + 2}

Add the numbers

9 x^{5}

9 x^{5} - x^{3} = 0

Factor the expression

x^{3} (9 x^{2} - 1) = 0

Separate the equation into 2 possible cases

x^{3} = 0 9 x^{2} - 1 = 0

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

x = 0 9 x^{2} - 1 = 0

Solve the equation

More Steps

Evaluate

9 x^{2} - 1 = 0

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

9 x^{2} = 0 + 1

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

9 x^{2} = 1

Divide both sides

\frac{9 x ^{2}}{9} = \frac{1}{9}

Divide the numbers

x^{2} = \frac{1}{9}

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

x = \pm \frac{1}{9}

Simplify the expression

More Steps

Evaluate

\frac{1}{9}

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

\frac{1}{9}

Simplify the radical expression

\frac{1}{9}

Simplify the radical expression

\frac{1}{3}

x = \pm \frac{1}{3}

Separate the equation into 2 possible cases

x = \frac{1}{3} x = - \frac{1}{3}

x = 0 x = \frac{1}{3} x = - \frac{1}{3}

Solution

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

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0, x_{3} = 0. \dot{3}

Show Solution