Solve (x-8) 2 (2x-5) (x^2)(x-8)

Question

Simplify the expression

4 x^{5} - 74 x^{4} + 416 x^{3} - 640 x^{2}

Evaluate

(x - 8) \times 2 (2 x - 5) x^{2} (x - 8)

Multiply the terms

(x - 8) \times 2 x^{2} (2 x - 5) (x - 8)

Multiply the first two terms

2 x^{2} (x - 8) (2 x - 5) (x - 8)

Multiply the terms

2 x^{2} (x - 8)^{2} (2 x - 5)

Expand the expression

More Steps

2 x^{2} (x^{2} - 16 x + 64) (2 x - 5)

Multiply the terms

More Steps

(2 x^{4} - 32 x^{3} + 128 x^{2}) (2 x - 5)

Apply the distributive property

2 x^{4} \times 2 x - 2 x^{4} \times 5 - 32 x^{3} \times 2 x - (- 32 x^{3} \times 5) + 128 x^{2} \times 2 x - 128 x^{2} \times 5

Multiply the terms

More Steps

4 x^{5} - 2 x^{4} \times 5 - 32 x^{3} \times 2 x - (- 32 x^{3} \times 5) + 128 x^{2} \times 2 x - 128 x^{2} \times 5

Multiply the numbers

4 x^{5} - 10 x^{4} - 32 x^{3} \times 2 x - (- 32 x^{3} \times 5) + 128 x^{2} \times 2 x - 128 x^{2} \times 5

Multiply the terms

More Steps

4 x^{5} - 10 x^{4} - 64 x^{4} - (- 32 x^{3} \times 5) + 128 x^{2} \times 2 x - 128 x^{2} \times 5

Multiply the numbers

4 x^{5} - 10 x^{4} - 64 x^{4} - (- 160 x^{3}) + 128 x^{2} \times 2 x - 128 x^{2} \times 5

Multiply the terms

More Steps

4 x^{5} - 10 x^{4} - 64 x^{4} - (- 160 x^{3}) + 256 x^{3} - 128 x^{2} \times 5

Multiply the numbers

4 x^{5} - 10 x^{4} - 64 x^{4} - (- 160 x^{3}) + 256 x^{3} - 640 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

4 x^{5} - 10 x^{4} - 64 x^{4} + 160 x^{3} + 256 x^{3} - 640 x^{2}

Subtract the terms

More Steps

4 x^{5} - 74 x^{4} + 160 x^{3} + 256 x^{3} - 640 x^{2}

Solution

More Steps

4 x^{5} - 74 x^{4} + 416 x^{3} - 640 x^{2}

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{5}{2}, x_{3} = 8

Alternative Form

x_{1} = 0, x_{2} = 2.5, x_{3} = 8

Show Solution