Solve 9w^3 18w^2-8w-16

Question

Simplify the expression

162 w^{5} - 8 w - 16

Evaluate

9 w^{3} \times 18 w^{2} - 8 w - 16

Solution

More Steps

Evaluate

9 w^{3} \times 18 w^{2}

Multiply the terms

162 w^{3} \times w^{2}

Multiply the terms with the same base by adding their exponents

162 w^{3 + 2}

Add the numbers

162 w^{5}

162 w^{5} - 8 w - 16

Show Solution

2 (3 w - 2) (27 w^{4} + 18 w^{3} + 12 w^{2} + 8 w + 4)

Evaluate

9 w^{3} \times 18 w^{2} - 8 w - 16

Multiply

More Steps

Evaluate

9 w^{3} \times 18 w^{2}

Multiply the terms

162 w^{3} \times w^{2}

Multiply the terms with the same base by adding their exponents

162 w^{3 + 2}

Add the numbers

162 w^{5}

162 w^{5} - 8 w - 16

Rewrite the expression

2 \times 81 w^{5} - 2 \times 4 w - 2 \times 8

Factor out 2 from the expression

2 (81 w^{5} - 4 w - 8)

Solution

More Steps

Evaluate

81 w^{5} - 4 w - 8

Calculate

81 w^{5} + 54 w^{4} + 36 w^{3} + 24 w^{2} + 12 w - 54 w^{4} - 36 w^{3} - 24 w^{2} - 16 w - 8

Rewrite the expression

3 w \times 27 w^{4} + 3 w \times 18 w^{3} + 3 w \times 12 w^{2} + 3 w \times 8 w + 3 w \times 4 - 2 \times 27 w^{4} - 2 \times 18 w^{3} - 2 \times 12 w^{2} - 2 \times 8 w - 2 \times 4

Factor out 3 w from the expression

3 w (27 w^{4} + 18 w^{3} + 12 w^{2} + 8 w + 4) - 2 \times 27 w^{4} - 2 \times 18 w^{3} - 2 \times 12 w^{2} - 2 \times 8 w - 2 \times 4

Factor out - 2 from the expression

3 w (27 w^{4} + 18 w^{3} + 12 w^{2} + 8 w + 4) - 2 (27 w^{4} + 18 w^{3} + 12 w^{2} + 8 w + 4)

Factor out 27 w^{4} + 18 w^{3} + 12 w^{2} + 8 w + 4 from the expression

(3 w - 2) (27 w^{4} + 18 w^{3} + 12 w^{2} + 8 w + 4)

2 (3 w - 2) (27 w^{4} + 18 w^{3} + 12 w^{2} + 8 w + 4)

Show Solution

w = \frac{2}{3}

Alternative Form

w = 0. \dot{6}

Evaluate

9 w^{3} \times 18 w^{2} - 8 w - 16

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

9 w^{3} \times 18 w^{2} - 8 w - 16 = 0

Multiply

More Steps

Multiply the terms

9 w^{3} \times 18 w^{2}

Multiply the terms

162 w^{3} \times w^{2}

Multiply the terms with the same base by adding their exponents

162 w^{3 + 2}

Add the numbers

162 w^{5}

162 w^{5} - 8 w - 16 = 0

Factor the expression

2 (3 w - 2) (27 w^{4} + 18 w^{3} + 12 w^{2} + 8 w + 4) = 0

Divide both sides

(3 w - 2) (27 w^{4} + 18 w^{3} + 12 w^{2} + 8 w + 4) = 0

Separate the equation into 2 possible cases

3 w - 2 = 0 27 w^{4} + 18 w^{3} + 12 w^{2} + 8 w + 4 = 0

Solve the equation

More Steps

Evaluate

3 w - 2 = 0

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

3 w = 0 + 2

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

3 w = 2

Divide both sides

\frac{3 w}{3} = \frac{2}{3}

Divide the numbers

w = \frac{2}{3}

w = \frac{2}{3} 27 w^{4} + 18 w^{3} + 12 w^{2} + 8 w + 4 = 0

Solve the equation

w = \frac{2}{3} w \in / R

Solution

w = \frac{2}{3}

Alternative Form

w = 0. \dot{6}

Show Solution