Solve (w^2 6w-3)(w^2)

Question

Simplify the expression

6 w^{5} - 3 w^{2}

Evaluate

(w^{2} \times 6 w - 3) w^{2}

Multiply

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Multiply the terms

w^{2} \times 6 w

Multiply the terms with the same base by adding their exponents

w^{2 + 1} \times 6

Add the numbers

w^{3} \times 6

Use the commutative property to reorder the terms

6 w^{3}

(6 w^{3} - 3) w^{2}

Multiply the terms

w^{2} (6 w^{3} - 3)

Apply the distributive property

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

Multiply the terms

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Evaluate

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

Use the commutative property to reorder the terms

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

Multiply the terms

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Evaluate

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

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

w^{2 + 3}

Add the numbers

w^{5}

6 w^{5}

6 w^{5} - w^{2} \times 3

Solution

6 w^{5} - 3 w^{2}

Show Solution

Factor the expression

3 w^{2} (2 w^{3} - 1)

Evaluate

(w^{2} \times 6 w - 3) w^{2}

Multiply

More Steps

Multiply the terms

w^{2} \times 6 w

Multiply the terms with the same base by adding their exponents

w^{2 + 1} \times 6

Add the numbers

w^{3} \times 6

Use the commutative property to reorder the terms

6 w^{3}

(6 w^{3} - 3) w^{2}

Multiply the terms

w^{2} (6 w^{3} - 3)

Factor the expression

w^{2} \times 3 (2 w^{3} - 1)

Solution

3 w^{2} (2 w^{3} - 1)

Show Solution

Find the roots

w_{1} = 0, w_{2} = \frac{3 4}{2}

Alternative Form

w_{1} = 0, w_{2} \approx 0.793701

Evaluate

(w^{2} \times 6 w - 3) (w^{2})

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

(w^{2} \times 6 w - 3) (w^{2}) = 0

Multiply

More Steps

Multiply the terms

w^{2} \times 6 w

Multiply the terms with the same base by adding their exponents

w^{2 + 1} \times 6

Add the numbers

w^{3} \times 6

Use the commutative property to reorder the terms

6 w^{3}

(6 w^{3} - 3) (w^{2}) = 0

Calculate

(6 w^{3} - 3) w^{2} = 0

Multiply the terms

w^{2} (6 w^{3} - 3) = 0

Separate the equation into 2 possible cases

w^{2} = 0 6 w^{3} - 3 = 0

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

w = 0 6 w^{3} - 3 = 0

Solve the equation

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Evaluate

6 w^{3} - 3 = 0

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

6 w^{3} = 0 + 3

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

6 w^{3} = 3

Divide both sides

\frac{6 w ^{3}}{6} = \frac{3}{6}

Divide the numbers

w^{3} = \frac{3}{6}

Cancel out the common factor 3

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

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

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

Calculate

w = 3 \frac{1}{2}

Simplify the root

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Evaluate

3 \frac{1}{2}

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

\frac{3 1}{3 2}

Simplify the radical expression

\frac{1}{3 2}

Multiply by the Conjugate

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

Simplify

\frac{3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

\frac{3 4}{2}

w = \frac{3 4}{2}

w = 0 w = \frac{3 4}{2}

Solution

w_{1} = 0, w_{2} = \frac{3 4}{2}

Alternative Form

w_{1} = 0, w_{2} \approx 0.793701

Show Solution