Solve 9\eta ^2 22\eta ^3-12\eta ^4

Question

Simplify the expression

Solution

198 η^{5} - 12 η^{4}

Evaluate

9 η^{2} \times 22 η^{3} - 12 η^{4}

Solution

More Steps

Evaluate

9 η^{2} \times 22 η^{3}

Multiply the terms

198 η^{2} \times η^{3}

Multiply the terms with the same base by adding their exponents

198 η^{2 + 3}

Add the numbers

198 η^{5}

198 η^{5} - 12 η^{4}

Show Solution

Factor the expression

Factor

6 η^{4} (33 η - 2)

Evaluate

9 η^{2} \times 22 η^{3} - 12 η^{4}

Multiply

More Steps

Evaluate

9 η^{2} \times 22 η^{3}

Multiply the terms

198 η^{2} \times η^{3}

Multiply the terms with the same base by adding their exponents

198 η^{2 + 3}

Add the numbers

198 η^{5}

198 η^{5} - 12 η^{4}

Rewrite the expression

6 η^{4} \times 33 η - 6 η^{4} \times 2

Solution

6 η^{4} (33 η - 2)

Show Solution

Find the roots

Find the roots of the algebra expression

η_{1} = 0, η_{2} = \frac{2}{33}

Alternative Form

η_{1} = 0, η_{2} = 0. \dot{0} \dot{6}

Evaluate

9 η^{2} \times 22 η^{3} - 12 η^{4}

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

9 η^{2} \times 22 η^{3} - 12 η^{4} = 0

Multiply

More Steps

Multiply the terms

9 η^{2} \times 22 η^{3}

Multiply the terms

198 η^{2} \times η^{3}

Multiply the terms with the same base by adding their exponents

198 η^{2 + 3}

Add the numbers

198 η^{5}

198 η^{5} - 12 η^{4} = 0

Factor the expression

6 η^{4} (33 η - 2) = 0

Divide both sides

η^{4} (33 η - 2) = 0

Separate the equation into 2 possible cases

η^{4} = 0 33 η - 2 = 0

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

η = 0 33 η - 2 = 0

Solve the equation

More Steps

Evaluate

33 η - 2 = 0

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

33 η = 0 + 2

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

33 η = 2

Divide both sides

\frac{33 η}{33} = \frac{2}{33}

Divide the numbers

η = \frac{2}{33}

η = 0 η = \frac{2}{33}

Solution

η_{1} = 0, η_{2} = \frac{2}{33}

Alternative Form

η_{1} = 0, η_{2} = 0. \dot{0} \dot{6}

Show Solution

9\eta ^2 22\eta ^3 12\eta ^4

Simplify the expression

Solution

Factor the expression

Factor

Find the roots

Find the roots of the algebra expression