Solve (3u-4) (u-7u-2)

Question

Simplify the expression

- 18 u^{2} + 18 u + 8

Evaluate

(3 u - 4) (u - 7 u - 2)

Subtract the terms

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Evaluate

u - 7 u

Collect like terms by calculating the sum or difference of their coefficients

(1 - 7) u

Subtract the numbers

- 6 u

(3 u - 4) (- 6 u - 2)

Apply the distributive property

3 u (- 6 u) - 3 u \times 2 - 4 (- 6 u) - (- 4 \times 2)

Multiply the terms

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Evaluate

3 u (- 6 u)

Multiply the numbers

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Evaluate

3 (- 6)

Multiplying or dividing an odd number of negative terms equals a negative

- 3 \times 6

Multiply the numbers

- 18

- 18 u \times u

Multiply the terms

- 18 u^{2}

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

Multiply the numbers

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

Multiply the numbers

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Evaluate

- 4 (- 6)

Multiplying or dividing an even number of negative terms equals a positive

4 \times 6

Multiply the numbers

24

- 18 u^{2} - 6 u + 24 u - (- 4 \times 2)

Multiply the numbers

- 18 u^{2} - 6 u + 24 u - (- 8)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 18 u^{2} - 6 u + 24 u + 8

Solution

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Evaluate

- 6 u + 24 u

Collect like terms by calculating the sum or difference of their coefficients

(- 6 + 24) u

Add the numbers

18 u

- 18 u^{2} + 18 u + 8

Show Solution

Factor the expression

- 2 (3 u - 4) (3 u + 1)

Evaluate

(3 u - 4) (u - 7 u - 2)

Subtract the terms

More Steps

Evaluate

u - 7 u

Collect like terms by calculating the sum or difference of their coefficients

(1 - 7) u

Subtract the numbers

- 6 u

(3 u - 4) (- 6 u - 2)

Factor the expression

(3 u - 4) (- 2) (3 u + 1)

Solution

- 2 (3 u - 4) (3 u + 1)

Show Solution

Find the roots

u_{1} = - \frac{1}{3}, u_{2} = \frac{4}{3}

Alternative Form

u_{1} = - 0. \dot{3}, u_{2} = 1. \dot{3}

Evaluate

(3 u - 4) (u - 7 u - 2)

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

(3 u - 4) (u - 7 u - 2) = 0

Subtract the terms

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Simplify

u - 7 u

Collect like terms by calculating the sum or difference of their coefficients

(1 - 7) u

Subtract the numbers

- 6 u

(3 u - 4) (- 6 u - 2) = 0

Separate the equation into 2 possible cases

3 u - 4 = 0 - 6 u - 2 = 0

Solve the equation

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Evaluate

3 u - 4 = 0

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

3 u = 0 + 4

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

3 u = 4

Divide both sides

\frac{3 u}{3} = \frac{4}{3}

Divide the numbers

u = \frac{4}{3}

u = \frac{4}{3} - 6 u - 2 = 0

Solve the equation

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Evaluate

- 6 u - 2 = 0

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

- 6 u = 0 + 2

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

- 6 u = 2

Change the signs on both sides of the equation

6 u = - 2

Divide both sides

\frac{6 u}{6} = \frac{- 2}{6}

Divide the numbers

u = \frac{- 2}{6}

Divide the numbers

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Evaluate

\frac{- 2}{6}

Cancel out the common factor 2

\frac{- 1}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{1}{3}

u = - \frac{1}{3}

u = \frac{4}{3} u = - \frac{1}{3}

Solution

u_{1} = - \frac{1}{3}, u_{2} = \frac{4}{3}

Alternative Form

u_{1} = - 0. \dot{3}, u_{2} = 1. \dot{3}

Show Solution