Solve 64s^6-1 - ScanMath

Question

Factor the expression

(2 s - 1) (4 s^{2} + 2 s + 1) (2 s + 1) (4 s^{2} - 2 s + 1)

Evaluate

64 s^{6} - 1

Rewrite the expression in exponential form

(8 s^{3})^{2} - 1^{2}

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

(8 s^{3} - 1) (8 s^{3} + 1)

Evaluate

More Steps

Evaluate

8 s^{3} - 1

Rewrite the expression in exponential form

(2 s)^{3} - 1^{3}

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

(2 s - 1) ((2 s)^{2} + 2 s \times 1 + 1^{2})

Evaluate

More Steps

Evaluate

(2 s)^{2}

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

2^{2} s^{2}

Evaluate the power

4 s^{2}

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

Any expression multiplied by 1 remains the same

(2 s - 1) (4 s^{2} + 2 s + 1^{2})

1 raised to any power equals to 1

(2 s - 1) (4 s^{2} + 2 s + 1)

(2 s - 1) (4 s^{2} + 2 s + 1) (8 s^{3} + 1)

Solution

More Steps

Evaluate

8 s^{3} + 1

Rewrite the expression in exponential form

(2 s)^{3} + 1^{3}

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

(2 s + 1) ((2 s)^{2} - 2 s \times 1 + 1^{2})

Evaluate

More Steps

Evaluate

(2 s)^{2}

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

2^{2} s^{2}

Evaluate the power

4 s^{2}

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

Any expression multiplied by 1 remains the same

(2 s + 1) (4 s^{2} - 2 s + 1^{2})

1 raised to any power equals to 1

(2 s + 1) (4 s^{2} - 2 s + 1)

(2 s - 1) (4 s^{2} + 2 s + 1) (2 s + 1) (4 s^{2} - 2 s + 1)

Show Solution

s_{1} = - \frac{1}{2}, s_{2} = \frac{1}{2}

Alternative Form

s_{1} = - 0.5, s_{2} = 0.5

Evaluate

64 s^{6} - 1

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

64 s^{6} - 1 = 0

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

64 s^{6} = 0 + 1

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

64 s^{6} = 1

Divide both sides

\frac{64 s ^{6}}{64} = \frac{1}{64}

Divide the numbers

s^{6} = \frac{1}{64}

Take the root of both sides of the equation and remember to use both positive and negative roots

s = \pm 6 \frac{1}{64}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{64}

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

\frac{6 1}{6 64}

Simplify the radical expression

\frac{1}{6 64}

Simplify the radical expression

More Steps

Evaluate

664

Write the number in exponential form with the base of 2

6 2^{6}

Reduce the index of the radical and exponent with 6

2

\frac{1}{2}

s = \pm \frac{1}{2}

Separate the equation into 2 possible cases

s = \frac{1}{2} s = - \frac{1}{2}

Solution

s_{1} = - \frac{1}{2}, s_{2} = \frac{1}{2}

Alternative Form

s_{1} = - 0.5, s_{2} = 0.5

Show Solution