Solve 3p^2p-p - ScanMath

Question

Simplify the expression

3 p^{3} - p

Evaluate

3 p^{2} \times p - p

Solution

More Steps

Evaluate

3 p^{2} \times p

Multiply the terms with the same base by adding their exponents

3 p^{2 + 1}

Add the numbers

3 p^{3}

3 p^{3} - p

Show Solution

p (3 p^{2} - 1)

Evaluate

3 p^{2} \times p - p

Multiply

More Steps

Evaluate

3 p^{2} \times p

Multiply the terms with the same base by adding their exponents

3 p^{2 + 1}

Add the numbers

3 p^{3}

3 p^{3} - p

Rewrite the expression

p \times 3 p^{2} - p

Solution

p (3 p^{2} - 1)

Show Solution

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

Alternative Form

p_{1} \approx - 0.57735, p_{2} = 0, p_{3} \approx 0.57735

Evaluate

3 p^{2} \times p - p

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

3 p^{2} \times p - p = 0

Multiply

More Steps

Multiply the terms

3 p^{2} \times p

Multiply the terms with the same base by adding their exponents

3 p^{2 + 1}

Add the numbers

3 p^{3}

3 p^{3} - p = 0

Factor the expression

p (3 p^{2} - 1) = 0

Separate the equation into 2 possible cases

p = 0 3 p^{2} - 1 = 0

Solve the equation

More Steps

Evaluate

3 p^{2} - 1 = 0

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

3 p^{2} = 0 + 1

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

3 p^{2} = 1

Divide both sides

\frac{3 p ^{2}}{3} = \frac{1}{3}

Divide the numbers

p^{2} = \frac{1}{3}

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

p = \pm \frac{1}{3}

Simplify the expression

More Steps

Evaluate

\frac{1}{3}

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

\frac{1}{3}

Simplify the radical expression

\frac{1}{3}

Multiply by the Conjugate

\frac{3}{3 \times 3}

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

\frac{3}{3}

p = \pm \frac{3}{3}

Separate the equation into 2 possible cases

p = \frac{3}{3} p = - \frac{3}{3}

p = 0 p = \frac{3}{3} p = - \frac{3}{3}

Solution

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

Alternative Form

p_{1} \approx - 0.57735, p_{2} = 0, p_{3} \approx 0.57735

Show Solution