Solve (m-1)( - 2m^22m-1)

Question

Simplify the expression

- 4 m^{4} - m + 4 m^{3} + 1

Evaluate

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

Multiply

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Evaluate

- 2 m^{2} \times 2 m

Multiply the terms

- 4 m^{2} \times m

Multiply the terms with the same base by adding their exponents

- 4 m^{2 + 1}

Add the numbers

- 4 m^{3}

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

Apply the distributive property

m (- 4 m^{3}) - m \times 1 - (- 4 m^{3}) - (- 1)

Multiply the terms

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Evaluate

m (- 4 m^{3})

Use the commutative property to reorder the terms

- 4 m \times m^{3}

Multiply the terms

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Evaluate

m \times m^{3}

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

m^{1 + 3}

Add the numbers

m^{4}

- 4 m^{4}

- 4 m^{4} - m \times 1 - (- 4 m^{3}) - (- 1)

Any expression multiplied by 1 remains the same

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

When there is - in front of an expression in parentheses change the sign of each term of the expression and remove the parentheses

- 4 m^{4} - m + 4 m^{3} - (- 1)

Solution

- 4 m^{4} - m + 4 m^{3} + 1

Show Solution

Find the roots

m_{1} = - \frac{3 2}{2}, m_{2} = 1

Alternative Form

m_{1} \approx - 0.629961, m_{2} = 1

Evaluate

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

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

(m - 1) (- 2 m^{2} \times 2 m - 1) = 0

Multiply

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Multiply the terms

- 2 m^{2} \times 2 m

Multiply the terms

- 4 m^{2} \times m

Multiply the terms with the same base by adding their exponents

- 4 m^{2 + 1}

Add the numbers

- 4 m^{3}

(m - 1) (- 4 m^{3} - 1) = 0

Separate the equation into 2 possible cases

m - 1 = 0 - 4 m^{3} - 1 = 0

Solve the equation

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Evaluate

m - 1 = 0

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

m = 0 + 1

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

m = 1

m = 1 - 4 m^{3} - 1 = 0

Solve the equation

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Evaluate

- 4 m^{3} - 1 = 0

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

- 4 m^{3} = 0 + 1

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

- 4 m^{3} = 1

Change the signs on both sides of the equation

4 m^{3} = - 1

Divide both sides

\frac{4 m ^{3}}{4} = \frac{- 1}{4}

Divide the numbers

m^{3} = \frac{- 1}{4}

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

m^{3} = - \frac{1}{4}

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

3 m^{3} = 3 - \frac{1}{4}

Calculate

m = 3 - \frac{1}{4}

Simplify the root

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Evaluate

3 - \frac{1}{4}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{4}

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

- \frac{3 1}{3 4}

Simplify the radical expression

- \frac{1}{3 4}

Multiply by the Conjugate

\frac{- 3 4 ^{2}}{3 4 \times 3 4 ^{2}}

Simplify

\frac{- 2 3 2}{3 4 \times 3 4 ^{2}}

Multiply the numbers

\frac{- 2 3 2}{2 ^{2}}

Reduce the fraction

\frac{- 3 2}{2}

Calculate

- \frac{3 2}{2}

m = - \frac{3 2}{2}

m = 1 m = - \frac{3 2}{2}

Solution

m_{1} = - \frac{3 2}{2}, m_{2} = 1

Alternative Form

m_{1} \approx - 0.629961, m_{2} = 1

Show Solution