Solve b^524-6b - ScanMath

Question

Simplify the expression

24 b^{5} - 6 b

Evaluate

b^{5} \times 24 - 6 b

Solution

24 b^{5} - 6 b

Show Solution

6 b (2 b^{2} - 1) (2 b^{2} + 1)

Evaluate

b^{5} \times 24 - 6 b

Use the commutative property to reorder the terms

24 b^{5} - 6 b

Factor out 6 b from the expression

6 b (4 b^{4} - 1)

Solution

More Steps

Evaluate

4 b^{4} - 1

Rewrite the expression in exponential form

(2 b^{2})^{2} - 1^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(2 b^{2} - 1) (2 b^{2} + 1)

6 b (2 b^{2} - 1) (2 b^{2} + 1)

Show Solution

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

Alternative Form

b_{1} \approx - 0.707107, b_{2} = 0, b_{3} \approx 0.707107

Evaluate

b^{5} \times 24 - 6 b

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

b^{5} \times 24 - 6 b = 0

Use the commutative property to reorder the terms

24 b^{5} - 6 b = 0

Factor the expression

6 b (4 b^{4} - 1) = 0

Divide both sides

b (4 b^{4} - 1) = 0

Separate the equation into 2 possible cases

b = 0 4 b^{4} - 1 = 0

Solve the equation

More Steps

Evaluate

4 b^{4} - 1 = 0

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

4 b^{4} = 0 + 1

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

4 b^{4} = 1

Divide both sides

\frac{4 b ^{4}}{4} = \frac{1}{4}

Divide the numbers

b^{4} = \frac{1}{4}

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

b = \pm 4 \frac{1}{4}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{4}

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

\frac{4 1}{4 4}

Simplify the radical expression

\frac{1}{4 4}

Simplify the radical expression

\frac{1}{2}

Multiply by the Conjugate

\frac{2}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{2}{2}

b = \pm \frac{2}{2}

Separate the equation into 2 possible cases

b = \frac{2}{2} b = - \frac{2}{2}

b = 0 b = \frac{2}{2} b = - \frac{2}{2}

Solution

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

Alternative Form

b_{1} \approx - 0.707107, b_{2} = 0, b_{3} \approx 0.707107

Show Solution