Solve 5m(5m^4 5m^2-4)

Question

Simplify the expression

125 m^{7} - 20 m

Evaluate

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

Multiply

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Evaluate

5 m^{4} \times 5 m^{2}

Multiply the terms

25 m^{4} \times m^{2}

Multiply the terms with the same base by adding their exponents

25 m^{4 + 2}

Add the numbers

25 m^{6}

5 m (25 m^{6} - 4)

Apply the distributive property

5 m \times 25 m^{6} - 5 m \times 4

Multiply the terms

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Evaluate

5 m \times 25 m^{6}

Multiply the numbers

125 m \times m^{6}

Multiply the terms

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Evaluate

m \times m^{6}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

m^{1 + 6}

Add the numbers

m^{7}

125 m^{7}

125 m^{7} - 5 m \times 4

Solution

125 m^{7} - 20 m

Show Solution

Factor the expression

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

Evaluate

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

Multiply

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Evaluate

5 m^{4} \times 5 m^{2}

Multiply the terms

25 m^{4} \times m^{2}

Multiply the terms with the same base by adding their exponents

25 m^{4 + 2}

Add the numbers

25 m^{6}

5 m (25 m^{6} - 4)

Solution

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

Show Solution

Find the roots

m_{1} = - \frac{3 50}{5}, m_{2} = 0, m_{3} = \frac{3 50}{5}

Alternative Form

m_{1} \approx - 0.736806, m_{2} = 0, m_{3} \approx 0.736806

Evaluate

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

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

5 m (5 m^{4} \times 5 m^{2} - 4) = 0

Multiply

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Multiply the terms

5 m^{4} \times 5 m^{2}

Multiply the terms

25 m^{4} \times m^{2}

Multiply the terms with the same base by adding their exponents

25 m^{4 + 2}

Add the numbers

25 m^{6}

5 m (25 m^{6} - 4) = 0

Elimination the left coefficient

m (25 m^{6} - 4) = 0

Separate the equation into 2 possible cases

m = 0 25 m^{6} - 4 = 0

Solve the equation

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Evaluate

25 m^{6} - 4 = 0

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

25 m^{6} = 0 + 4

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

25 m^{6} = 4

Divide both sides

\frac{25 m ^{6}}{25} = \frac{4}{25}

Divide the numbers

m^{6} = \frac{4}{25}

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

m = \pm 6 \frac{4}{25}

Simplify the expression

More Steps

Evaluate

6 \frac{4}{25}

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

\frac{6 4}{6 25}

Simplify the radical expression

\frac{3 2}{6 25}

Simplify the radical expression

\frac{3 2}{3 5}

Multiply by the Conjugate

\frac{3 2 \times 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{3 2 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

\frac{3 50}{3 5 \times 3 5 ^{2}}

Multiply the numbers

\frac{3 50}{5}

m = \pm \frac{3 50}{5}

Separate the equation into 2 possible cases

m = \frac{3 50}{5} m = - \frac{3 50}{5}

m = 0 m = \frac{3 50}{5} m = - \frac{3 50}{5}

Solution

m_{1} = - \frac{3 50}{5}, m_{2} = 0, m_{3} = \frac{3 50}{5}

Alternative Form

m_{1} \approx - 0.736806, m_{2} = 0, m_{3} \approx 0.736806

Show Solution