Solve 27y^(3)-125

Question

Factor the expression

(3 y - 5) (9 y^{2} + 15 y + 25)

Evaluate

27 y^{3} - 125

Rewrite the expression in exponential form

(3 y)^{3} - 5^{3}

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

(3 y - 5) ((3 y)^{2} + 3 y \times 5 + 5^{2})

Evaluate

More Steps

Evaluate

(3 y)^{2}

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

3^{2} y^{2}

Evaluate the power

9 y^{2}

(3 y - 5) (9 y^{2} + 3 y \times 5 + 5^{2})

Evaluate

(3 y - 5) (9 y^{2} + 15 y + 5^{2})

Solution

(3 y - 5) (9 y^{2} + 15 y + 25)

Show Solution

y = \frac{5}{3}

Alternative Form

y = 1. \dot{6}

Evaluate

27 y^{3} - 125

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

27 y^{3} - 125 = 0

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

27 y^{3} = 0 + 125

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

27 y^{3} = 125

Divide both sides

\frac{27 y ^{3}}{27} = \frac{125}{27}

Divide the numbers

y^{3} = \frac{125}{27}

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

3 y^{3} = 3 \frac{125}{27}

Calculate

y = 3 \frac{125}{27}

Solution

More Steps

Evaluate

3 \frac{125}{27}

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

\frac{3 125}{3 27}

Simplify the radical expression

More Steps

Evaluate

3125

Write the number in exponential form with the base of 5

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{5}{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{5}{3}

y = \frac{5}{3}

Alternative Form

y = 1. \dot{6}

Show Solution