Solve r^38-2r - ScanMath

Question

Simplify the expression

8 r^{3} - 2 r

Evaluate

r^{3} \times 8 - 2 r

Solution

8 r^{3} - 2 r

Show Solution

2 r (2 r - 1) (2 r + 1)

Evaluate

r^{3} \times 8 - 2 r

Use the commutative property to reorder the terms

8 r^{3} - 2 r

Factor out 2 r from the expression

2 r (4 r^{2} - 1)

Solution

More Steps

Evaluate

4 r^{2} - 1

Rewrite the expression in exponential form

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

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

(2 r - 1) (2 r + 1)

2 r (2 r - 1) (2 r + 1)

Show Solution

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

Alternative Form

r_{1} = - 0.5, r_{2} = 0, r_{3} = 0.5

Evaluate

r^{3} \times 8 - 2 r

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

r^{3} \times 8 - 2 r = 0

Use the commutative property to reorder the terms

8 r^{3} - 2 r = 0

Factor the expression

2 r (4 r^{2} - 1) = 0

Divide both sides

r (4 r^{2} - 1) = 0

Separate the equation into 2 possible cases

r = 0 4 r^{2} - 1 = 0

Solve the equation

More Steps

Evaluate

4 r^{2} - 1 = 0

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

4 r^{2} = 0 + 1

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

4 r^{2} = 1

Divide both sides

\frac{4 r ^{2}}{4} = \frac{1}{4}

Divide the numbers

r^{2} = \frac{1}{4}

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

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

Simplify the expression

More Steps

Evaluate

\frac{1}{4}

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

\frac{1}{4}

Simplify the radical expression

\frac{1}{4}

Simplify the radical expression

\frac{1}{2}

r = \pm \frac{1}{2}

Separate the equation into 2 possible cases

r = \frac{1}{2} r = - \frac{1}{2}

r = 0 r = \frac{1}{2} r = - \frac{1}{2}

Solution

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

Alternative Form

r_{1} = - 0.5, r_{2} = 0, r_{3} = 0.5

Show Solution