Solve 9b^3 b - 4b

Question

Simplify the expression

9 b^{4} - 4 b

Evaluate

9 b^{3} \times b - 4 b

Solution

More Steps

Evaluate

9 b^{3} \times b

Multiply the terms with the same base by adding their exponents

9 b^{3 + 1}

Add the numbers

9 b^{4}

9 b^{4} - 4 b

Show Solution

Factor the expression

b (9 b^{3} - 4)

Evaluate

9 b^{3} \times b - 4 b

Multiply

More Steps

Evaluate

9 b^{3} \times b

Multiply the terms with the same base by adding their exponents

9 b^{3 + 1}

Add the numbers

9 b^{4}

9 b^{4} - 4 b

Rewrite the expression

b \times 9 b^{3} - b \times 4

Solution

b (9 b^{3} - 4)

Show Solution

Find the roots

b_{1} = 0, b_{2} = \frac{3 12}{3}

Alternative Form

b_{1} = 0, b_{2} \approx 0.763143

Evaluate

9 b^{3} \times b - 4 b

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

9 b^{3} \times b - 4 b = 0

Multiply

More Steps

Multiply the terms

9 b^{3} \times b

Multiply the terms with the same base by adding their exponents

9 b^{3 + 1}

Add the numbers

9 b^{4}

9 b^{4} - 4 b = 0

Factor the expression

b (9 b^{3} - 4) = 0

Separate the equation into 2 possible cases

b = 0 9 b^{3} - 4 = 0

Solve the equation

More Steps

Evaluate

9 b^{3} - 4 = 0

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

9 b^{3} = 0 + 4

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

9 b^{3} = 4

Divide both sides

\frac{9 b ^{3}}{9} = \frac{4}{9}

Divide the numbers

b^{3} = \frac{4}{9}

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

3 b^{3} = 3 \frac{4}{9}

Calculate

b = 3 \frac{4}{9}

Simplify the root

More Steps

Evaluate

3 \frac{4}{9}

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

\frac{3 4}{3 9}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

\frac{3 3 12}{3 9 \times 3 9 ^{2}}

Multiply the numbers

\frac{3 3 12}{3 ^{2}}

Reduce the fraction

\frac{3 12}{3}

b = \frac{3 12}{3}

b = 0 b = \frac{3 12}{3}

Solution

b_{1} = 0, b_{2} = \frac{3 12}{3}

Alternative Form

b_{1} = 0, b_{2} \approx 0.763143

Show Solution