Solve r^2-2r^33r^2

Question

Simplify the expression

r^{2} - 6 r^{5}

Evaluate

r^{2} - 2 r^{3} \times 3 r^{2}

Solution

More Steps

Evaluate

2 r^{3} \times 3 r^{2}

Multiply the terms

6 r^{3} \times r^{2}

Multiply the terms with the same base by adding their exponents

6 r^{3 + 2}

Add the numbers

6 r^{5}

r^{2} - 6 r^{5}

Show Solution

Factor the expression

r^{2} (1 - 6 r^{3})

Evaluate

r^{2} - 2 r^{3} \times 3 r^{2}

Multiply

More Steps

Evaluate

2 r^{3} \times 3 r^{2}

Multiply the terms

6 r^{3} \times r^{2}

Multiply the terms with the same base by adding their exponents

6 r^{3 + 2}

Add the numbers

6 r^{5}

r^{2} - 6 r^{5}

Rewrite the expression

r^{2} - r^{2} \times 6 r^{3}

Solution

r^{2} (1 - 6 r^{3})

Show Solution

Find the roots

r_{1} = 0, r_{2} = \frac{3 36}{6}

Alternative Form

r_{1} = 0, r_{2} \approx 0.550321

Evaluate

r^{2} - 2 r^{3} \times 3 r^{2}

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

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

Multiply

More Steps

Multiply the terms

2 r^{3} \times 3 r^{2}

Multiply the terms

6 r^{3} \times r^{2}

Multiply the terms with the same base by adding their exponents

6 r^{3 + 2}

Add the numbers

6 r^{5}

r^{2} - 6 r^{5} = 0

Factor the expression

r^{2} (1 - 6 r^{3}) = 0

Separate the equation into 2 possible cases

r^{2} = 0 1 - 6 r^{3} = 0

The only way a power can be 0 is when the base equals 0

r = 0 1 - 6 r^{3} = 0

Solve the equation

More Steps

Evaluate

1 - 6 r^{3} = 0

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

- 6 r^{3} = 0 - 1

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

- 6 r^{3} = - 1

Change the signs on both sides of the equation

6 r^{3} = 1

Divide both sides

\frac{6 r ^{3}}{6} = \frac{1}{6}

Divide the numbers

r^{3} = \frac{1}{6}

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

3 r^{3} = 3 \frac{1}{6}

Calculate

r = 3 \frac{1}{6}

Simplify the root

More Steps

Evaluate

3 \frac{1}{6}

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

\frac{3 1}{3 6}

Simplify the radical expression

\frac{1}{3 6}

Multiply by the Conjugate

\frac{3 6 ^{2}}{3 6 \times 3 6 ^{2}}

Simplify

\frac{3 36}{3 6 \times 3 6 ^{2}}

Multiply the numbers

\frac{3 36}{6}

r = \frac{3 36}{6}

r = 0 r = \frac{3 36}{6}

Solution

r_{1} = 0, r_{2} = \frac{3 36}{6}

Alternative Form

r_{1} = 0, r_{2} \approx 0.550321

Show Solution