Solve 27y^3 - 27y^29y - 1

Question

Simplify the expression

- 216 y^{3} - 1

Evaluate

27 y^{3} - 27 y^{2} \times 9 y - 1

Multiply

More Steps

Multiply the terms

- 27 y^{2} \times 9 y

Multiply the terms

- 243 y^{2} \times y

Multiply the terms with the same base by adding their exponents

- 243 y^{2 + 1}

Add the numbers

- 243 y^{3}

27 y^{3} - 243 y^{3} - 1

Solution

More Steps

Evaluate

27 y^{3} - 243 y^{3}

Collect like terms by calculating the sum or difference of their coefficients

(27 - 243) y^{3}

Subtract the numbers

- 216 y^{3}

- 216 y^{3} - 1

Show Solution

Factor the expression

- (6 y + 1) (36 y^{2} - 6 y + 1)

Evaluate

27 y^{3} - 27 y^{2} \times 9 y - 1

Multiply

More Steps

Multiply the terms

27 y^{2} \times 9 y

Multiply the terms

243 y^{2} \times y

Multiply the terms with the same base by adding their exponents

243 y^{2 + 1}

Add the numbers

243 y^{3}

27 y^{3} - 243 y^{3} - 1

Subtract the terms

More Steps

Simplify

27 y^{3} - 243 y^{3}

Collect like terms by calculating the sum or difference of their coefficients

(27 - 243) y^{3}

Subtract the numbers

- 216 y^{3}

- 216 y^{3} - 1

Factor out - 1 from the expression

- (216 y^{3} + 1)

Solution

More Steps

Evaluate

216 y^{3} + 1

Calculate

216 y^{3} - 36 y^{2} + 6 y + 36 y^{2} - 6 y + 1

Rewrite the expression

6 y \times 36 y^{2} - 6 y \times 6 y + 6 y + 36 y^{2} - 6 y + 1

Factor out 6 y from the expression

6 y (36 y^{2} - 6 y + 1) + 36 y^{2} - 6 y + 1

Factor out 36 y^{2} - 6 y + 1 from the expression

(6 y + 1) (36 y^{2} - 6 y + 1)

- (6 y + 1) (36 y^{2} - 6 y + 1)

Show Solution

Find the roots

y = - \frac{1}{6}

Alternative Form

y = - 0.1 \dot{6}

Evaluate

27 y^{3} - 27 y^{2} \times 9 y - 1

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

27 y^{3} - 27 y^{2} \times 9 y - 1 = 0

Multiply

More Steps

Multiply the terms

27 y^{2} \times 9 y

Multiply the terms

243 y^{2} \times y

Multiply the terms with the same base by adding their exponents

243 y^{2 + 1}

Add the numbers

243 y^{3}

27 y^{3} - 243 y^{3} - 1 = 0

Subtract the terms

More Steps

Simplify

27 y^{3} - 243 y^{3}

Collect like terms by calculating the sum or difference of their coefficients

(27 - 243) y^{3}

Subtract the numbers

- 216 y^{3}

- 216 y^{3} - 1 = 0

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

- 216 y^{3} = 0 + 1

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

- 216 y^{3} = 1

Change the signs on both sides of the equation

216 y^{3} = - 1

Divide both sides

\frac{216 y ^{3}}{216} = \frac{- 1}{216}

Divide the numbers

y^{3} = \frac{- 1}{216}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

y^{3} = - \frac{1}{216}

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

3 y^{3} = 3 - \frac{1}{216}

Calculate

y = 3 - \frac{1}{216}

Solution

More Steps

Evaluate

3 - \frac{1}{216}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{216}

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

- \frac{3 1}{3 216}

Simplify the radical expression

- \frac{1}{3 216}

Simplify the radical expression

More Steps

Evaluate

3216

Write the number in exponential form with the base of 6

3 6^{3}

Reduce the index of the radical and exponent with 3

6

- \frac{1}{6}

y = - \frac{1}{6}

Alternative Form

y = - 0.1 \dot{6}

Show Solution