Solve (3m^(2) m-4)(-2m^(2)-3m 1)

Question

Simplify the expression

- 6 m^{5} - 9 m^{4} + 8 m^{2} + 12 m

Evaluate

(3 m^{2} \times m - 4) (- 2 m^{2} - 3 m \times 1)

Multiply

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Multiply the terms

3 m^{2} \times m

Multiply the terms with the same base by adding their exponents

3 m^{2 + 1}

Add the numbers

3 m^{3}

(3 m^{3} - 4) (- 2 m^{2} - 3 m \times 1)

Multiply the terms

(3 m^{3} - 4) (- 2 m^{2} - 3 m)

Apply the distributive property

3 m^{3} (- 2 m^{2}) - 3 m^{3} \times 3 m - 4 (- 2 m^{2}) - (- 4 \times 3 m)

Multiply the terms

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Evaluate

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

Multiply the numbers

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Evaluate

3 (- 2)

Multiplying or dividing an odd number of negative terms equals a negative

- 3 \times 2

Multiply the numbers

- 6

- 6 m^{3} \times m^{2}

Multiply the terms

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Evaluate

m^{3} \times m^{2}

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

m^{3 + 2}

Add the numbers

m^{5}

- 6 m^{5}

- 6 m^{5} - 3 m^{3} \times 3 m - 4 (- 2 m^{2}) - (- 4 \times 3 m)

Multiply the terms

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Evaluate

3 m^{3} \times 3 m

Multiply the numbers

9 m^{3} \times m

Multiply the terms

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Evaluate

m^{3} \times m

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

m^{3 + 1}

Add the numbers

m^{4}

9 m^{4}

- 6 m^{5} - 9 m^{4} - 4 (- 2 m^{2}) - (- 4 \times 3 m)

Multiply the numbers

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Evaluate

- 4 (- 2)

Multiplying or dividing an even number of negative terms equals a positive

4 \times 2

Multiply the numbers

8

- 6 m^{5} - 9 m^{4} + 8 m^{2} - (- 4 \times 3 m)

Multiply the numbers

- 6 m^{5} - 9 m^{4} + 8 m^{2} - (- 12 m)

Solution

- 6 m^{5} - 9 m^{4} + 8 m^{2} + 12 m

Show Solution

Factor the expression

- m (3 m^{3} - 4) (2 m + 3)

Evaluate

(3 m^{2} \times m - 4) (- 2 m^{2} - 3 m \times 1)

Multiply

More Steps

Multiply the terms

3 m^{2} \times m

Multiply the terms with the same base by adding their exponents

3 m^{2 + 1}

Add the numbers

3 m^{3}

(3 m^{3} - 4) (- 2 m^{2} - 3 m \times 1)

Multiply the terms

(3 m^{3} - 4) (- 2 m^{2} - 3 m)

Factor the expression

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Evaluate

- 2 m^{2} - 3 m

Rewrite the expression

- m \times 2 m - m \times 3

Factor out - m from the expression

- m (2 m + 3)

(3 m^{3} - 4) (- m) (2 m + 3)

Solution

- m (3 m^{3} - 4) (2 m + 3)

Show Solution

Find the roots

m_{1} = - \frac{3}{2}, m_{2} = 0, m_{3} = \frac{3 36}{3}

Alternative Form

m_{1} = - 1.5, m_{2} = 0, m_{3} \approx 1.100642

Evaluate

(3 m^{2} \times m - 4) (- 2 m^{2} - 3 m \times 1)

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

(3 m^{2} \times m - 4) (- 2 m^{2} - 3 m \times 1) = 0

Multiply

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Multiply the terms

3 m^{2} \times m

Multiply the terms with the same base by adding their exponents

3 m^{2 + 1}

Add the numbers

3 m^{3}

(3 m^{3} - 4) (- 2 m^{2} - 3 m \times 1) = 0

Multiply the terms

(3 m^{3} - 4) (- 2 m^{2} - 3 m) = 0

Separate the equation into 2 possible cases

3 m^{3} - 4 = 0 - 2 m^{2} - 3 m = 0

Solve the equation

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Evaluate

3 m^{3} - 4 = 0

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

3 m^{3} = 0 + 4

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

3 m^{3} = 4

Divide both sides

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

Divide the numbers

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

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

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

Calculate

m = 3 \frac{4}{3}

Simplify the root

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Evaluate

3 \frac{4}{3}

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

\frac{3 4}{3 3}

Multiply by the Conjugate

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

Simplify

\frac{3 4 \times 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

\frac{3 36}{3 3 \times 3 3 ^{2}}

Multiply the numbers

\frac{3 36}{3}

m = \frac{3 36}{3}

m = \frac{3 36}{3} - 2 m^{2} - 3 m = 0

Solve the equation

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Evaluate

- 2 m^{2} - 3 m = 0

Factor the expression

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Evaluate

- 2 m^{2} - 3 m

Rewrite the expression

- m \times 2 m - m \times 3

Factor out - m from the expression

- m (2 m + 3)

- m (2 m + 3) = 0

When the product of factors equals 0,at least one factor is 0

- m = 0 2 m + 3 = 0

Solve the equation for m

m = 0 2 m + 3 = 0

Solve the equation for m

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Evaluate

2 m + 3 = 0

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

2 m = 0 - 3

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

2 m = - 3

Divide both sides

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

Divide the numbers

m = \frac{- 3}{2}

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

m = - \frac{3}{2}

m = 0 m = - \frac{3}{2}

m = \frac{3 36}{3} m = 0 m = - \frac{3}{2}

Solution

m_{1} = - \frac{3}{2}, m_{2} = 0, m_{3} = \frac{3 36}{3}

Alternative Form

m_{1} = - 1.5, m_{2} = 0, m_{3} \approx 1.100642

Show Solution