Solve 4 -12x 9x^2

Question

Simplify the expression

4 - 108 x^{3}

Evaluate

4 - 12 x \times 9 x^{2}

Solution

More Steps

Evaluate

12 x \times 9 x^{2}

Multiply the terms

108 x \times x^{2}

Multiply the terms with the same base by adding their exponents

108 x^{1 + 2}

Add the numbers

108 x^{3}

4 - 108 x^{3}

Show Solution

Factor the expression

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

Evaluate

4 - 12 x \times 9 x^{2}

Evaluate

More Steps

Evaluate

12 x \times 9 x^{2}

Multiply the terms

108 x \times x^{2}

Multiply the terms with the same base by adding their exponents

108 x^{1 + 2}

Add the numbers

108 x^{3}

4 - 108 x^{3}

Factor out 4 from the expression

4 (1 - 27 x^{3})

Solution

More Steps

Evaluate

1 - 27 x^{3}

Rewrite the expression in exponential form

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

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

(1 - 3 x) (1^{2} + 1 \times 3 x + (3 x)^{2})

1 raised to any power equals to 1

(1 - 3 x) (1 + 1 \times 3 x + (3 x)^{2})

Any expression multiplied by 1 remains the same

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

Evaluate

More Steps

Evaluate

(3 x)^{2}

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

3^{2} x^{2}

Evaluate the power

9 x^{2}

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

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

Show Solution

Find the roots

x = \frac{1}{3}

Alternative Form

x = 0. \dot{3}

Evaluate

4 - 12 x \times 9 x^{2}

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

4 - 12 x \times 9 x^{2} = 0

Multiply

More Steps

Multiply the terms

12 x \times 9 x^{2}

Multiply the terms

108 x \times x^{2}

Multiply the terms with the same base by adding their exponents

108 x^{1 + 2}

Add the numbers

108 x^{3}

4 - 108 x^{3} = 0

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

- 108 x^{3} = 0 - 4

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

- 108 x^{3} = - 4

Change the signs on both sides of the equation

108 x^{3} = 4

Divide both sides

\frac{108 x ^{3}}{108} = \frac{4}{108}

Divide the numbers

x^{3} = \frac{4}{108}

Cancel out the common factor 4

x^{3} = \frac{1}{27}

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

3 x^{3} = 3 \frac{1}{27}

Calculate

x = 3 \frac{1}{27}

Solution

More Steps

Evaluate

3 \frac{1}{27}

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

\frac{3 1}{3 27}

Simplify the radical expression

\frac{1}{3 27}

Simplify the radical expression

More Steps

Evaluate

327

Write the number in exponential form with the base of 3

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{1}{3}

x = \frac{1}{3}

Alternative Form

x = 0. \dot{3}

Show Solution