Solve 125m^6-1 - ScanMath

Question

Factor the expression

(5 m^{2} - 1) (25 m^{4} + 5 m^{2} + 1)

Evaluate

125 m^{6} - 1

Rewrite the expression in exponential form

(5 m^{2})^{3} - 1^{3}

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

(5 m^{2} - 1) ((5 m^{2})^{2} + 5 m^{2} \times 1 + 1^{2})

Evaluate

More Steps

Evaluate

(5 m^{2})^{2}

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

5^{2} (m^{2})^{2}

Evaluate the power

25 (m^{2})^{2}

Evaluate the power

More Steps

Evaluate

(m^{2})^{2}

Multiply the exponents

m^{2 \times 2}

Multiply the terms

m^{4}

25 m^{4}

(5 m^{2} - 1) (25 m^{4} + 5 m^{2} \times 1 + 1^{2})

Any expression multiplied by 1 remains the same

(5 m^{2} - 1) (25 m^{4} + 5 m^{2} + 1^{2})

Solution

(5 m^{2} - 1) (25 m^{4} + 5 m^{2} + 1)

Show Solution

m_{1} = - \frac{5}{5}, m_{2} = \frac{5}{5}

Alternative Form

m_{1} \approx - 0.447214, m_{2} \approx 0.447214

Evaluate

125 m^{6} - 1

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

125 m^{6} - 1 = 0

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

125 m^{6} = 0 + 1

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

125 m^{6} = 1

Divide both sides

\frac{125 m ^{6}}{125} = \frac{1}{125}

Divide the numbers

m^{6} = \frac{1}{125}

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

m = \pm 6 \frac{1}{125}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{125}

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

\frac{6 1}{6 125}

Simplify the radical expression

\frac{1}{6 125}

Simplify the radical expression

More Steps

Evaluate

6125

Write the number in exponential form with the base of 5

6 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{1}{5}

Multiply by the Conjugate

\frac{5}{5 \times 5}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{5}{5}

m = \pm \frac{5}{5}

Separate the equation into 2 possible cases

m = \frac{5}{5} m = - \frac{5}{5}

Solution

m_{1} = - \frac{5}{5}, m_{2} = \frac{5}{5}

Alternative Form

m_{1} \approx - 0.447214, m_{2} \approx 0.447214

Show Solution