Solve 2b^3 3b^2 - 12b

Question

Simplify the expression

6 b^{5} - 12 b

Evaluate

2 b^{3} \times 3 b^{2} - 12 b

Solution

More Steps

Evaluate

2 b^{3} \times 3 b^{2}

Multiply the terms

6 b^{3} \times b^{2}

Multiply the terms with the same base by adding their exponents

6 b^{3 + 2}

Add the numbers

6 b^{5}

6 b^{5} - 12 b

Show Solution

6 b (b^{4} - 2)

Evaluate

2 b^{3} \times 3 b^{2} - 12 b

Multiply

More Steps

Evaluate

2 b^{3} \times 3 b^{2}

Multiply the terms

6 b^{3} \times b^{2}

Multiply the terms with the same base by adding their exponents

6 b^{3 + 2}

Add the numbers

6 b^{5}

6 b^{5} - 12 b

Rewrite the expression

6 b \times b^{4} - 6 b \times 2

Solution

6 b (b^{4} - 2)

Show Solution

b_{1} = - 42, b_{2} = 0, b_{3} = 42

Alternative Form

b_{1} \approx - 1.189207, b_{2} = 0, b_{3} \approx 1.189207

Evaluate

2 b^{3} \times 3 b^{2} - 12 b

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

2 b^{3} \times 3 b^{2} - 12 b = 0

Multiply

More Steps

Multiply the terms

2 b^{3} \times 3 b^{2}

Multiply the terms

6 b^{3} \times b^{2}

Multiply the terms with the same base by adding their exponents

6 b^{3 + 2}

Add the numbers

6 b^{5}

6 b^{5} - 12 b = 0

Factor the expression

6 b (b^{4} - 2) = 0

Divide both sides

b (b^{4} - 2) = 0

Separate the equation into 2 possible cases

b = 0 b^{4} - 2 = 0

Solve the equation

More Steps

Evaluate

b^{4} - 2 = 0

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

b^{4} = 0 + 2

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

b^{4} = 2

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

b = \pm 42

Separate the equation into 2 possible cases

b = 42 b = - 42

b = 0 b = 42 b = - 42

Solution

b_{1} = - 42, b_{2} = 0, b_{3} = 42

Alternative Form

b_{1} \approx - 1.189207, b_{2} = 0, b_{3} \approx 1.189207

Show Solution