Solve (x-4)(x-1-i)(x-1 i)

Question

Simplify the expression

x^{3} + (- 5 - 2 i) x^{2} + (3 + 9 i) x + 4 - 4 i

Evaluate

(x - 4) (x - 1 - i) (x - 1 \times i)

Any expression multiplied by 1 remains the same

(x - 4) (x - 1 - i) (x - i)

Multiply the terms

More Steps

(x^{2} + (- 5 - i) x + 4 + 4 i) (x - i)

Apply the distributive property

x^{2} \times x - x^{2} i + (- 5 - i) x \times x - (- 5 - i) x i + (4 + 4 i) x - (4 + 4 i) i

Multiply the terms

More Steps

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

Use the commutative property to reorder the terms

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

Multiply the terms

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

Multiply the numbers

More Steps

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

Multiply the numbers

More Steps

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

Subtract the terms

More Steps

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

Solution

More Steps

x^{3} + (- 5 - 2 i) x^{2} + (3 + 9 i) x + 4 - 4 i

Show Solution