Solve 64y^(3)-1 - ScanMath

Question

Factor the expression

(4 y - 1) (16 y^{2} + 4 y + 1)

Evaluate

64 y^{3} - 1

Rewrite the expression in exponential form

(4 y)^{3} - 1^{3}

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

(4 y - 1) ((4 y)^{2} + 4 y \times 1 + 1^{2})

Evaluate

More Steps

Evaluate

(4 y)^{2}

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

4^{2} y^{2}

Evaluate the power

16 y^{2}

(4 y - 1) (16 y^{2} + 4 y \times 1 + 1^{2})

Any expression multiplied by 1 remains the same

(4 y - 1) (16 y^{2} + 4 y + 1^{2})

Solution

(4 y - 1) (16 y^{2} + 4 y + 1)

Show Solution

y = \frac{1}{4}

Alternative Form

y = 0.25

Evaluate

64 y^{3} - 1

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

64 y^{3} - 1 = 0

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

64 y^{3} = 0 + 1

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

64 y^{3} = 1

Divide both sides

\frac{64 y ^{3}}{64} = \frac{1}{64}

Divide the numbers

y^{3} = \frac{1}{64}

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

3 y^{3} = 3 \frac{1}{64}

Calculate

y = 3 \frac{1}{64}

Solution

More Steps

Evaluate

3 \frac{1}{64}

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

\frac{3 1}{3 64}

Simplify the radical expression

\frac{1}{3 64}

Simplify the radical expression

More Steps

Evaluate

364

Write the number in exponential form with the base of 4

3 4^{3}

Reduce the index of the radical and exponent with 3

4

\frac{1}{4}

y = \frac{1}{4}

Alternative Form

y = 0.25

Show Solution