Solve (x^2-2x)^2 3(x-1)

Question

Simplify the expression

3 x^{5} - 15 x^{4} + 24 x^{3} - 12 x^{2}

Evaluate

(x^{2} - 2 x)^{2} \times 3 (x - 1)

Use the commutative property to reorder the terms

3 (x^{2} - 2 x)^{2} (x - 1)

Expand the expression

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3 (x^{4} - 4 x^{3} + 4 x^{2}) (x - 1)

Multiply the terms

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(3 x^{4} - 12 x^{3} + 12 x^{2}) (x - 1)

Apply the distributive property

3 x^{4} \times x - 3 x^{4} \times 1 - 12 x^{3} \times x - (- 12 x^{3} \times 1) + 12 x^{2} \times x - 12 x^{2} \times 1

Multiply the terms

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3 x^{5} - 3 x^{4} \times 1 - 12 x^{3} \times x - (- 12 x^{3} \times 1) + 12 x^{2} \times x - 12 x^{2} \times 1

Any expression multiplied by 1 remains the same

3 x^{5} - 3 x^{4} - 12 x^{3} \times x - (- 12 x^{3} \times 1) + 12 x^{2} \times x - 12 x^{2} \times 1

Multiply the terms

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3 x^{5} - 3 x^{4} - 12 x^{4} - (- 12 x^{3} \times 1) + 12 x^{2} \times x - 12 x^{2} \times 1

Any expression multiplied by 1 remains the same

3 x^{5} - 3 x^{4} - 12 x^{4} - (- 12 x^{3}) + 12 x^{2} \times x - 12 x^{2} \times 1

Multiply the terms

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3 x^{5} - 3 x^{4} - 12 x^{4} - (- 12 x^{3}) + 12 x^{3} - 12 x^{2} \times 1

Any expression multiplied by 1 remains the same

3 x^{5} - 3 x^{4} - 12 x^{4} - (- 12 x^{3}) + 12 x^{3} - 12 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

3 x^{5} - 3 x^{4} - 12 x^{4} + 12 x^{3} + 12 x^{3} - 12 x^{2}

Subtract the terms

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3 x^{5} - 15 x^{4} + 12 x^{3} + 12 x^{3} - 12 x^{2}

Solution

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3 x^{5} - 15 x^{4} + 24 x^{3} - 12 x^{2}

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Factor the expression

3 x^{2} (x - 2)^{2} (x - 1)

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Find the roots

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

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