Solve (3x^(2)-12x 15)⋅(x-2)^(3)

Question

Simplify the expression

3 x^{5} - 198 x^{4} + 1116 x^{3} - 2184 x^{2} + 1440 x

Evaluate

(3 x^{2} - 12 x \times 15) (x - 2)^{3}

Multiply the terms

(3 x^{2} - 180 x) (x - 2)^{3}

Expand the expression

More Steps

(3 x^{2} - 180 x) (x^{3} - 6 x^{2} + 12 x - 8)

Apply the distributive property

3 x^{2} \times x^{3} - 3 x^{2} \times 6 x^{2} + 3 x^{2} \times 12 x - 3 x^{2} \times 8 - 180 x \times x^{3} - (- 180 x \times 6 x^{2}) - 180 x \times 12 x - (- 180 x \times 8)

Multiply the terms

More Steps

3 x^{5} - 3 x^{2} \times 6 x^{2} + 3 x^{2} \times 12 x - 3 x^{2} \times 8 - 180 x \times x^{3} - (- 180 x \times 6 x^{2}) - 180 x \times 12 x - (- 180 x \times 8)

Multiply the terms

More Steps

3 x^{5} - 18 x^{4} + 3 x^{2} \times 12 x - 3 x^{2} \times 8 - 180 x \times x^{3} - (- 180 x \times 6 x^{2}) - 180 x \times 12 x - (- 180 x \times 8)

Multiply the terms

More Steps

3 x^{5} - 18 x^{4} + 36 x^{3} - 3 x^{2} \times 8 - 180 x \times x^{3} - (- 180 x \times 6 x^{2}) - 180 x \times 12 x - (- 180 x \times 8)

Multiply the numbers

3 x^{5} - 18 x^{4} + 36 x^{3} - 24 x^{2} - 180 x \times x^{3} - (- 180 x \times 6 x^{2}) - 180 x \times 12 x - (- 180 x \times 8)

Multiply the terms

More Steps

3 x^{5} - 18 x^{4} + 36 x^{3} - 24 x^{2} - 180 x^{4} - (- 180 x \times 6 x^{2}) - 180 x \times 12 x - (- 180 x \times 8)

Multiply the terms

More Steps

3 x^{5} - 18 x^{4} + 36 x^{3} - 24 x^{2} - 180 x^{4} - (- 1080 x^{3}) - 180 x \times 12 x - (- 180 x \times 8)

Multiply the terms

More Steps

3 x^{5} - 18 x^{4} + 36 x^{3} - 24 x^{2} - 180 x^{4} - (- 1080 x^{3}) - 2160 x^{2} - (- 180 x \times 8)

Multiply the numbers

3 x^{5} - 18 x^{4} + 36 x^{3} - 24 x^{2} - 180 x^{4} - (- 1080 x^{3}) - 2160 x^{2} - (- 1440 x)

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

3 x^{5} - 18 x^{4} + 36 x^{3} - 24 x^{2} - 180 x^{4} + 1080 x^{3} - 2160 x^{2} + 1440 x

Subtract the terms

More Steps

3 x^{5} - 198 x^{4} + 36 x^{3} - 24 x^{2} + 1080 x^{3} - 2160 x^{2} + 1440 x

Add the terms

More Steps

3 x^{5} - 198 x^{4} + 1116 x^{3} - 24 x^{2} - 2160 x^{2} + 1440 x

Solution

More Steps

3 x^{5} - 198 x^{4} + 1116 x^{3} - 2184 x^{2} + 1440 x

Show Solution

Factor the expression

3 x (x - 60) (x - 2)^{3}

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Find the roots

x_{1} = 0, x_{2} = 2, x_{3} = 60

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