Solve n^3-2-(n^3-3n^2)

Question

Simplify the expression

- 2 + 3 n^{2}

Evaluate

n^{3} - 2 - (n^{3} - 3 n^{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

n^{3} - 2 - n^{3} + 3 n^{2}

The sum of two opposites equals 0

More Steps

Evaluate

n^{3} - n^{3}

Collect like terms

(1 - 1) n^{3}

Add the coefficients

0 \times n^{3}

Calculate

0

0 - 2 + 3 n^{2}

Solution

- 2 + 3 n^{2}

Show Solution

Find the roots

n_{1} = - \frac{6}{3}, n_{2} = \frac{6}{3}

Alternative Form

n_{1} \approx - 0.816497, n_{2} \approx 0.816497

Evaluate

n^{3} - 2 - (n^{3} - 3 n^{2})

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

n^{3} - 2 - (n^{3} - 3 n^{2}) = 0

Subtract the terms

More Steps

Simplify

n^{3} - 2 - (n^{3} - 3 n^{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

n^{3} - 2 - n^{3} + 3 n^{2}

The sum of two opposites equals 0

More Steps

Evaluate

n^{3} - n^{3}

Collect like terms

(1 - 1) n^{3}

Add the coefficients

0 \times n^{3}

Calculate

0

0 - 2 + 3 n^{2}

Remove 0

- 2 + 3 n^{2}

- 2 + 3 n^{2} = 0

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

3 n^{2} = 0 + 2

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

3 n^{2} = 2

Divide both sides

\frac{3 n ^{2}}{3} = \frac{2}{3}

Divide the numbers

n^{2} = \frac{2}{3}

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

n = \pm \frac{2}{3}

Simplify the expression

More Steps

Evaluate

\frac{2}{3}

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

\frac{2}{3}

Multiply by the Conjugate

\frac{2 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

2 \times 3

The product of roots with the same index is equal to the root of the product

2 \times 3

Calculate the product

6

\frac{6}{3 \times 3}

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

\frac{6}{3}

n = \pm \frac{6}{3}

Separate the equation into 2 possible cases

n = \frac{6}{3} n = - \frac{6}{3}

Solution

n_{1} = - \frac{6}{3}, n_{2} = \frac{6}{3}

Alternative Form

n_{1} \approx - 0.816497, n_{2} \approx 0.816497

Show Solution