Solve x * (11-2x)(8-2x)

Question

Simplify the expression

88 x - 38 x^{2} + 4 x^{3}

Evaluate

x (11 - 2 x) (8 - 2 x)

Multiply the terms

More Steps

Evaluate

x (11 - 2 x)

Apply the distributive property

x \times 11 - x \times 2 x

Use the commutative property to reorder the terms

11 x - x \times 2 x

Multiply the terms

More Steps

Evaluate

x \times 2 x

Use the commutative property to reorder the terms

2 x \times x

Multiply the terms

2 x^{2}

11 x - 2 x^{2}

(11 x - 2 x^{2}) (8 - 2 x)

Apply the distributive property

11 x \times 8 - 11 x \times 2 x - 2 x^{2} \times 8 - (- 2 x^{2} \times 2 x)

Multiply the numbers

88 x - 11 x \times 2 x - 2 x^{2} \times 8 - (- 2 x^{2} \times 2 x)

Multiply the terms

More Steps

Evaluate

11 x \times 2 x

Multiply the numbers

22 x \times x

Multiply the terms

22 x^{2}

88 x - 22 x^{2} - 2 x^{2} \times 8 - (- 2 x^{2} \times 2 x)

Multiply the numbers

88 x - 22 x^{2} - 16 x^{2} - (- 2 x^{2} \times 2 x)

Multiply the terms

More Steps

Evaluate

- 2 x^{2} \times 2 x

Multiply the numbers

- 4 x^{2} \times x

Multiply the terms

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Evaluate

x^{2} \times x

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

x^{2 + 1}

Add the numbers

x^{3}

- 4 x^{3}

88 x - 22 x^{2} - 16 x^{2} - (- 4 x^{3})

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

88 x - 22 x^{2} - 16 x^{2} + 4 x^{3}

Solution

More Steps

Evaluate

- 22 x^{2} - 16 x^{2}

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

(- 22 - 16) x^{2}

Subtract the numbers

- 38 x^{2}

88 x - 38 x^{2} + 4 x^{3}

Show Solution

Factor the expression

2 x (11 - 2 x) (4 - x)

Evaluate

x (11 - 2 x) (8 - 2 x)

Factor the expression

x (11 - 2 x) \times 2 (4 - x)

Solution

2 x (11 - 2 x) (4 - x)

Show Solution

Find the roots

x_{1} = 0, x_{2} = 4, x_{3} = \frac{11}{2}

Alternative Form

x_{1} = 0, x_{2} = 4, x_{3} = 5.5

Evaluate

x (11 - 2 x) (8 - 2 x)

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

x (11 - 2 x) (8 - 2 x) = 0

Separate the equation into 3 possible cases

x = 0 11 - 2 x = 0 8 - 2 x = 0

Solve the equation

More Steps

Evaluate

11 - 2 x = 0

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

- 2 x = 0 - 11

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

- 2 x = - 11

Change the signs on both sides of the equation

2 x = 11

Divide both sides

\frac{2 x}{2} = \frac{11}{2}

Divide the numbers

x = \frac{11}{2}

x = 0 x = \frac{11}{2} 8 - 2 x = 0

Solve the equation

More Steps

Evaluate

8 - 2 x = 0

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

- 2 x = 0 - 8

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

- 2 x = - 8

Change the signs on both sides of the equation

2 x = 8

Divide both sides

\frac{2 x}{2} = \frac{8}{2}

Divide the numbers

x = \frac{8}{2}

Divide the numbers

More Steps

Evaluate

\frac{8}{2}

Reduce the numbers

\frac{4}{1}

Calculate

4

x = 4

x = 0 x = \frac{11}{2} x = 4

Solution

x_{1} = 0, x_{2} = 4, x_{3} = \frac{11}{2}

Alternative Form

x_{1} = 0, x_{2} = 4, x_{3} = 5.5

Show Solution