Solve (x-1)(x^3)(x-2)(x-6) 96

Question

Simplify the expression

96 x^{6} - 864 x^{5} + 1920 x^{4} - 1152 x^{3}

Evaluate

(x - 1) x^{3} (x - 2) (x - 6) \times 96

Use the commutative property to reorder the terms

(x - 1) \times 96 x^{3} (x - 2) (x - 6)

Multiply the first two terms

96 x^{3} (x - 1) (x - 2) (x - 6)

Multiply the terms

More Steps

(96 x^{4} - 96 x^{3}) (x - 2) (x - 6)

Multiply the terms

More Steps

(96 x^{5} - 288 x^{4} + 192 x^{3}) (x - 6)

Apply the distributive property

96 x^{5} \times x - 96 x^{5} \times 6 - 288 x^{4} \times x - (- 288 x^{4} \times 6) + 192 x^{3} \times x - 192 x^{3} \times 6

Multiply the terms

More Steps

96 x^{6} - 96 x^{5} \times 6 - 288 x^{4} \times x - (- 288 x^{4} \times 6) + 192 x^{3} \times x - 192 x^{3} \times 6

Multiply the numbers

96 x^{6} - 576 x^{5} - 288 x^{4} \times x - (- 288 x^{4} \times 6) + 192 x^{3} \times x - 192 x^{3} \times 6

Multiply the terms

More Steps

96 x^{6} - 576 x^{5} - 288 x^{5} - (- 288 x^{4} \times 6) + 192 x^{3} \times x - 192 x^{3} \times 6

Multiply the numbers

96 x^{6} - 576 x^{5} - 288 x^{5} - (- 1728 x^{4}) + 192 x^{3} \times x - 192 x^{3} \times 6

Multiply the terms

More Steps

96 x^{6} - 576 x^{5} - 288 x^{5} - (- 1728 x^{4}) + 192 x^{4} - 192 x^{3} \times 6

Multiply the numbers

96 x^{6} - 576 x^{5} - 288 x^{5} - (- 1728 x^{4}) + 192 x^{4} - 1152 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

96 x^{6} - 576 x^{5} - 288 x^{5} + 1728 x^{4} + 192 x^{4} - 1152 x^{3}

Subtract the terms

More Steps

96 x^{6} - 864 x^{5} + 1728 x^{4} + 192 x^{4} - 1152 x^{3}

Solution

More Steps

96 x^{6} - 864 x^{5} + 1920 x^{4} - 1152 x^{3}

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Find the roots

x_{1} = 0, x_{2} = 1, x_{3} = 2, x_{4} = 6

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