Solve 32- 8x (8-2x)(4-x)

Question

Simplify the expression

32 - 256 x + 128 x^{2} - 16 x^{3}

Evaluate

32 - 8 x (8 - 2 x) (4 - x)

Solution

More Steps

Calculate

- 8 x (8 - 2 x) (4 - x)

Simplify

More Steps

Evaluate

- 8 x (8 - 2 x)

Apply the distributive property

- 8 x \times 8 - (- 8 x \times 2 x)

Multiply the numbers

- 64 x - (- 8 x \times 2 x)

Multiply the terms

- 64 x - (- 16 x^{2})

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

- 64 x + 16 x^{2}

(- 64 x + 16 x^{2}) (4 - x)

Apply the distributive property

- 64 x \times 4 - (- 64 x \times x) + 16 x^{2} \times 4 - 16 x^{2} \times x

Multiply the numbers

- 256 x - (- 64 x \times x) + 16 x^{2} \times 4 - 16 x^{2} \times x

Multiply the terms

- 256 x - (- 64 x^{2}) + 16 x^{2} \times 4 - 16 x^{2} \times x

Multiply the numbers

- 256 x - (- 64 x^{2}) + 64 x^{2} - 16 x^{2} \times x

Multiply the terms

More Steps

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}

- 256 x - (- 64 x^{2}) + 64 x^{2} - 16 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

- 256 x + 64 x^{2} + 64 x^{2} - 16 x^{3}

Add the terms

More Steps

Evaluate

64 x^{2} + 64 x^{2}

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

(64 + 64) x^{2}

Add the numbers

128 x^{2}

- 256 x + 128 x^{2} - 16 x^{3}

32 - 256 x + 128 x^{2} - 16 x^{3}

Show Solution

Factor the expression

16 (2 - 16 x + 8 x^{2} - x^{3})

Evaluate

32 - 8 x (8 - 2 x) (4 - x)

Simplify

More Steps

Evaluate

- 8 x (8 - 2 x) (4 - x)

Simplify

More Steps

Evaluate

- 8 x (8 - 2 x)

Apply the distributive property

- 8 x \times 8 - 8 x (- 2 x)

Multiply the terms

- 64 x - 8 x (- 2 x)

Multiply the terms

- 64 x + 16 x^{2}

(- 64 x + 16 x^{2}) (4 - x)

Apply the distributive property

- 64 x \times 4 - 64 x (- x) + 16 x^{2} \times 4 + 16 x^{2} (- x)

Multiply the terms

- 256 x - 64 x (- x) + 16 x^{2} \times 4 + 16 x^{2} (- x)

Multiply the terms

More Steps

Evaluate

- 64 x (- x)

Multiply the numbers

64 x \times x

Multiply the terms

64 x^{2}

- 256 x + 64 x^{2} + 16 x^{2} \times 4 + 16 x^{2} (- x)

Multiply the terms

- 256 x + 64 x^{2} + 64 x^{2} + 16 x^{2} (- x)

Multiply the terms

More Steps

Evaluate

16 x^{2} (- x)

Multiply the numbers

- 16 x^{2} \times x

Multiply the terms

- 16 x^{3}

- 256 x + 64 x^{2} + 64 x^{2} - 16 x^{3}

32 - 256 x + 64 x^{2} + 64 x^{2} - 16 x^{3}

Add the terms

More Steps

Evaluate

64 x^{2} + 64 x^{2}

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

(64 + 64) x^{2}

Add the numbers

128 x^{2}

32 - 256 x + 128 x^{2} - 16 x^{3}

Solution

16 (2 - 16 x + 8 x^{2} - x^{3})

Show Solution

Find the roots

x_{1} \approx 0.133802, x_{2} \approx 3.210756, x_{3} \approx 4.655442

Evaluate

32 - 8 x (8 - 2 x) (4 - x)

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

32 - 8 x (8 - 2 x) (4 - x) = 0

Calculate

More Steps

Calculate

- 8 x (8 - 2 x) (4 - x)

Simplify

More Steps

Evaluate

- 8 x (8 - 2 x)

Apply the distributive property

- 8 x \times 8 - (- 8 x \times 2 x)

Multiply the numbers

- 64 x - (- 8 x \times 2 x)

Multiply the terms

- 64 x - (- 16 x^{2})

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

- 64 x + 16 x^{2}

(- 64 x + 16 x^{2}) (4 - x)

Apply the distributive property

- 64 x \times 4 - (- 64 x \times x) + 16 x^{2} \times 4 - 16 x^{2} \times x

Multiply the numbers

- 256 x - (- 64 x \times x) + 16 x^{2} \times 4 - 16 x^{2} \times x

Multiply the terms

- 256 x - (- 64 x^{2}) + 16 x^{2} \times 4 - 16 x^{2} \times x

Multiply the numbers

- 256 x - (- 64 x^{2}) + 64 x^{2} - 16 x^{2} \times x

Multiply the terms

More Steps

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}

- 256 x - (- 64 x^{2}) + 64 x^{2} - 16 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

- 256 x + 64 x^{2} + 64 x^{2} - 16 x^{3}

Add the terms

More Steps

Evaluate

64 x^{2} + 64 x^{2}

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

(64 + 64) x^{2}

Add the numbers

128 x^{2}

- 256 x + 128 x^{2} - 16 x^{3}

32 - 256 x + 128 x^{2} - 16 x^{3} = 0

Factor the expression

16 (2 - 16 x + 8 x^{2} - x^{3}) = 0

Divide both sides

2 - 16 x + 8 x^{2} - x^{3} = 0

Calculate

x \approx 0.133802 x \approx 3.210756 x \approx 4.655442

Solution

x_{1} \approx 0.133802, x_{2} \approx 3.210756, x_{3} \approx 4.655442

Show Solution