Solve 8x^3-27 - ScanMath

Question

Factor the expression

(2 x - 3) (4 x^{2} + 6 x + 9)

Evaluate

8 x^{3} - 27

Rewrite the expression in exponential form

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

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

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

Evaluate

More Steps

Evaluate

(2 x)^{2}

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

2^{2} x^{2}

Evaluate the power

4 x^{2}

(2 x - 3) (4 x^{2} + 2 x \times 3 + 3^{2})

Evaluate

(2 x - 3) (4 x^{2} + 6 x + 3^{2})

Solution

(2 x - 3) (4 x^{2} + 6 x + 9)

Show Solution

x = \frac{3}{2}

Alternative Form

x = 1.5

Evaluate

8 x^{3} - 27

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

8 x^{3} - 27 = 0

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

8 x^{3} = 0 + 27

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

8 x^{3} = 27

Divide both sides

\frac{8 x ^{3}}{8} = \frac{27}{8}

Divide the numbers

x^{3} = \frac{27}{8}

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

3 x^{3} = 3 \frac{27}{8}

Calculate

x = 3 \frac{27}{8}

Solution

More Steps

Evaluate

3 \frac{27}{8}

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

\frac{3 27}{3 8}

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{3}{3 8}

Simplify the radical expression

More Steps

Evaluate

38

Write the number in exponential form with the base of 2

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3}{2}

x = \frac{3}{2}

Alternative Form

x = 1.5

Show Solution