Solve (3u-2)(3u+2)

Question

Simplify the expression

9 u^{2} - 4

Evaluate

(3 u - 2) (3 u + 2)

Use (a - b) (a + b) = a^{2} - b^{2} to simplify the product

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

Evaluate the power

More Steps

Evaluate

(3 u)^{2}

To raise a product to a power,raise each factor to that power

3^{2} u^{2}

Evaluate the power

9 u^{2}

9 u^{2} - 2^{2}

Solution

9 u^{2} - 4

Show Solution

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

Alternative Form

u_{1} = - 0. \dot{6}, u_{2} = 0. \dot{6}

Evaluate

(3 u - 2) (3 u + 2)

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

(3 u - 2) (3 u + 2) = 0

Separate the equation into 2 possible cases

3 u - 2 = 0 3 u + 2 = 0

Solve the equation

More Steps

Evaluate

3 u - 2 = 0

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

3 u = 0 + 2

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

3 u = 2

Divide both sides

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

Divide the numbers

u = \frac{2}{3}

u = \frac{2}{3} 3 u + 2 = 0

Solve the equation

More Steps

Evaluate

3 u + 2 = 0

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

3 u = 0 - 2

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

3 u = - 2

Divide both sides

\frac{3 u}{3} = \frac{- 2}{3}

Divide the numbers

u = \frac{- 2}{3}

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

u = - \frac{2}{3}

u = \frac{2}{3} u = - \frac{2}{3}

Solution

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

Alternative Form

u_{1} = - 0. \dot{6}, u_{2} = 0. \dot{6}

Show Solution