Solve (x 1)(x-8)(x-6)(x (-i)(x-(-i)))

Question

Simplify the expression

- i x^{5} + (1 + 14 i) x^{4} + (- 14 - 48 i) x^{3} + 48 x^{2}

Evaluate

(x \times 1) (x - 8) (x - 6) (x (- i) (x - (- i)))

Remove the parentheses

x \times 1 \times (x - 8) (x - 6) x (- i) (x - (- i))

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

x \times 1 \times (x - 8) (x - 6) x (- i) (x + i)

Rewrite the expression

x (x - 8) (x - 6) x (- i) (x + i)

Rewrite the expression

- x (x - 8) (x - 6) x i (x + i)

Multiply the terms

- x^{2} (x - 8) (x - 6) i (x + i)

Use the commutative property to reorder the terms

- i x^{2} (x - 8) (x - 6) (x + i)

Multiply the terms

More Steps

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

Multiply the terms

More Steps

(- i x^{4} + 14 i x^{3} - 48 i x^{2}) (x + i)

Apply the distributive property

- i x^{4} \times x - i x^{4} i + 14 i x^{3} \times x + 14 i x^{3} i - 48 i x^{2} \times x - 48 i x^{2} i

Multiply the terms

More Steps

- i x^{5} - i x^{4} i + 14 i x^{3} \times x + 14 i x^{3} i - 48 i x^{2} \times x - 48 i x^{2} i

Multiply the numbers

More Steps

- i x^{5} + x^{4} + 14 i x^{3} \times x + 14 i x^{3} i - 48 i x^{2} \times x - 48 i x^{2} i

Multiply the terms

More Steps

- i x^{5} + x^{4} + 14 i x^{4} + 14 i x^{3} i - 48 i x^{2} \times x - 48 i x^{2} i

Multiply the numbers

More Steps

- i x^{5} + x^{4} + 14 i x^{4} - 14 x^{3} - 48 i x^{2} \times x - 48 i x^{2} i

Multiply the terms

More Steps

- i x^{5} + x^{4} + 14 i x^{4} - 14 x^{3} - 48 i x^{3} - 48 i x^{2} i

Multiply the numbers

More Steps

- i x^{5} + x^{4} + 14 i x^{4} - 14 x^{3} - 48 i x^{3} + 48 x^{2}

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

- i x^{5} + (1 + 14 i) x^{4} - 14 x^{3} - 48 i x^{3} + 48 x^{2}

Solution

- i x^{5} + (1 + 14 i) x^{4} + (- 14 - 48 i) x^{3} + 48 x^{2}

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