Solve (4m^3)(-16m^2 12m-9)

Question

Simplify the expression

- 768 m^{6} - 36 m^{3}

Evaluate

4 m^{3} (- 16 m^{2} \times 12 m - 9)

Multiply

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Evaluate

- 16 m^{2} \times 12 m

Multiply the terms

- 192 m^{2} \times m

Multiply the terms with the same base by adding their exponents

- 192 m^{2 + 1}

Add the numbers

- 192 m^{3}

4 m^{3} (- 192 m^{3} - 9)

Apply the distributive property

4 m^{3} (- 192 m^{3}) - 4 m^{3} \times 9

Multiply the terms

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Evaluate

4 m^{3} (- 192 m^{3})

Multiply the numbers

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Evaluate

4 (- 192)

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

- 4 \times 192

Multiply the numbers

- 768

- 768 m^{3} \times m^{3}

Multiply the terms

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Evaluate

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

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

m^{3 + 3}

Add the numbers

m^{6}

- 768 m^{6}

- 768 m^{6} - 4 m^{3} \times 9

Solution

- 768 m^{6} - 36 m^{3}

Show Solution

Factor the expression

- 12 m^{3} (64 m^{3} + 3)

Evaluate

4 m^{3} (- 16 m^{2} \times 12 m - 9)

Multiply

More Steps

Evaluate

- 16 m^{2} \times 12 m

Multiply the terms

- 192 m^{2} \times m

Multiply the terms with the same base by adding their exponents

- 192 m^{2 + 1}

Add the numbers

- 192 m^{3}

4 m^{3} (- 192 m^{3} - 9)

Factor the expression

4 m^{3} (- 3) (64 m^{3} + 3)

Solution

- 12 m^{3} (64 m^{3} + 3)

Show Solution

Find the roots

m_{1} = - \frac{3 3}{4}, m_{2} = 0

Alternative Form

m_{1} \approx - 0.360562, m_{2} = 0

Evaluate

(4 m^{3}) (- 16 m^{2} \times 12 m - 9)

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

(4 m^{3}) (- 16 m^{2} \times 12 m - 9) = 0

Multiply the terms

4 m^{3} (- 16 m^{2} \times 12 m - 9) = 0

Multiply

More Steps

Multiply the terms

- 16 m^{2} \times 12 m

Multiply the terms

- 192 m^{2} \times m

Multiply the terms with the same base by adding their exponents

- 192 m^{2 + 1}

Add the numbers

- 192 m^{3}

4 m^{3} (- 192 m^{3} - 9) = 0

Elimination the left coefficient

m^{3} (- 192 m^{3} - 9) = 0

Separate the equation into 2 possible cases

m^{3} = 0 - 192 m^{3} - 9 = 0

The only way a power can be 0 is when the base equals 0

m = 0 - 192 m^{3} - 9 = 0

Solve the equation

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Evaluate

- 192 m^{3} - 9 = 0

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

- 192 m^{3} = 0 + 9

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

- 192 m^{3} = 9

Change the signs on both sides of the equation

192 m^{3} = - 9

Divide both sides

\frac{192 m ^{3}}{192} = \frac{- 9}{192}

Divide the numbers

m^{3} = \frac{- 9}{192}

Divide the numbers

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Evaluate

\frac{- 9}{192}

Cancel out the common factor 3

\frac{- 3}{64}

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

- \frac{3}{64}

m^{3} = - \frac{3}{64}

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

3 m^{3} = 3 - \frac{3}{64}

Calculate

m = 3 - \frac{3}{64}

Simplify the root

More Steps

Evaluate

3 - \frac{3}{64}

An odd root of a negative radicand is always a negative

- 3 \frac{3}{64}

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

- \frac{3 3}{3 64}

Simplify the radical expression

- \frac{3 3}{4}

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

m = 0 m = - \frac{3 3}{4}

Solution

m_{1} = - \frac{3 3}{4}, m_{2} = 0

Alternative Form

m_{1} \approx - 0.360562, m_{2} = 0

Show Solution