Solve (4u^(2) 5u-2)⋅(u-6)

Question

Simplify the expression

20 u^{4} - 120 u^{3} - 2 u + 12

Evaluate

(4 u^{2} \times 5 u - 2) (u - 6)

Multiply

More Steps

Evaluate

4 u^{2} \times 5 u

Multiply the terms

20 u^{2} \times u

Multiply the terms with the same base by adding their exponents

20 u^{2 + 1}

Add the numbers

20 u^{3}

(20 u^{3} - 2) (u - 6)

Apply the distributive property

20 u^{3} \times u - 20 u^{3} \times 6 - 2 u - (- 2 \times 6)

Multiply the terms

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Evaluate

u^{3} \times u

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

u^{3 + 1}

Add the numbers

u^{4}

20 u^{4} - 20 u^{3} \times 6 - 2 u - (- 2 \times 6)

Multiply the numbers

20 u^{4} - 120 u^{3} - 2 u - (- 2 \times 6)

Multiply the numbers

20 u^{4} - 120 u^{3} - 2 u - (- 12)

Solution

20 u^{4} - 120 u^{3} - 2 u + 12

Show Solution

Factor the expression

2 (10 u^{3} - 1) (u - 6)

Evaluate

(4 u^{2} \times 5 u - 2) (u - 6)

Multiply

More Steps

Evaluate

4 u^{2} \times 5 u

Multiply the terms

20 u^{2} \times u

Multiply the terms with the same base by adding their exponents

20 u^{2 + 1}

Add the numbers

20 u^{3}

(20 u^{3} - 2) (u - 6)

Solution

2 (10 u^{3} - 1) (u - 6)

Show Solution

Find the roots

u_{1} = \frac{3 100}{10}, u_{2} = 6

Alternative Form

u_{1} \approx 0.464159, u_{2} = 6

Evaluate

(4 u^{2} \times 5 u - 2) (u - 6)

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

(4 u^{2} \times 5 u - 2) (u - 6) = 0

Multiply

More Steps

Multiply the terms

4 u^{2} \times 5 u

Multiply the terms

20 u^{2} \times u

Multiply the terms with the same base by adding their exponents

20 u^{2 + 1}

Add the numbers

20 u^{3}

(20 u^{3} - 2) (u - 6) = 0

Separate the equation into 2 possible cases

20 u^{3} - 2 = 0 u - 6 = 0

Solve the equation

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Evaluate

20 u^{3} - 2 = 0

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

20 u^{3} = 0 + 2

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

20 u^{3} = 2

Divide both sides

\frac{20 u ^{3}}{20} = \frac{2}{20}

Divide the numbers

u^{3} = \frac{2}{20}

Cancel out the common factor 2

u^{3} = \frac{1}{10}

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

3 u^{3} = 3 \frac{1}{10}

Calculate

u = 3 \frac{1}{10}

Simplify the root

More Steps

Evaluate

3 \frac{1}{10}

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

\frac{3 1}{3 10}

Simplify the radical expression

\frac{1}{3 10}

Multiply by the Conjugate

\frac{3 1 0 ^{2}}{3 10 \times 3 1 0 ^{2}}

Simplify

\frac{3 100}{3 10 \times 3 1 0 ^{2}}

Multiply the numbers

\frac{3 100}{10}

u = \frac{3 100}{10}

u = \frac{3 100}{10} u - 6 = 0

Solve the equation

More Steps

Evaluate

u - 6 = 0

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

u = 0 + 6

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

u = 6

u = \frac{3 100}{10} u = 6

Solution

u_{1} = \frac{3 100}{10}, u_{2} = 6

Alternative Form

u_{1} \approx 0.464159, u_{2} = 6

Show Solution