Solve (x-3)(x-3)(x^3i)(x-3i)

Question

Simplify the expression

i x^{6} + (3 - 6 i) x^{5} + (- 18 + 9 i) x^{4} + 27 x^{3}

Evaluate

(x - 3) (x - 3) (x^{3} i) (x - 3 i)

Remove the parentheses

(x - 3) (x - 3) x^{3} i (x - 3 i)

Use the commutative property to reorder the terms

(x - 3) (x - 3) i x^{3} (x - 3 i)

Multiply the first two terms

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

Use the commutative property to reorder the terms

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

Expand the expression

More Steps

i x^{3} (x^{2} - 6 x + 9) (x - 3 i)

Multiply the terms

More Steps

(i x^{5} - 6 i x^{4} + 9 i x^{3}) (x - 3 i)

Apply the distributive property

i x^{5} \times x - i x^{5} \times 3 i - 6 i x^{4} \times x - (- 6 i x^{4} \times 3 i) + 9 i x^{3} \times x - 9 i x^{3} \times 3 i

Multiply the terms

More Steps

i x^{6} - i x^{5} \times 3 i - 6 i x^{4} \times x - (- 6 i x^{4} \times 3 i) + 9 i x^{3} \times x - 9 i x^{3} \times 3 i

Multiply the numbers

More Steps

i x^{6} - (- 3 x^{5}) - 6 i x^{4} \times x - (- 6 i x^{4} \times 3 i) + 9 i x^{3} \times x - 9 i x^{3} \times 3 i

Multiply the terms

More Steps

i x^{6} - (- 3 x^{5}) - 6 i x^{5} - (- 6 i x^{4} \times 3 i) + 9 i x^{3} \times x - 9 i x^{3} \times 3 i

Multiply the numbers

More Steps

i x^{6} - (- 3 x^{5}) - 6 i x^{5} - 18 x^{4} + 9 i x^{3} \times x - 9 i x^{3} \times 3 i

Multiply the terms

More Steps

i x^{6} - (- 3 x^{5}) - 6 i x^{5} - 18 x^{4} + 9 i x^{4} - 9 i x^{3} \times 3 i

Multiply the numbers

More Steps

i x^{6} - (- 3 x^{5}) - 6 i x^{5} - 18 x^{4} + 9 i x^{4} - (- 27 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

i x^{6} + 3 x^{5} - 6 i x^{5} - 18 x^{4} + 9 i x^{4} + 27 x^{3}

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

i x^{6} + (3 - 6 i) x^{5} - 18 x^{4} + 9 i x^{4} + 27 x^{3}

Solution

i x^{6} + (3 - 6 i) x^{5} + (- 18 + 9 i) x^{4} + 27 x^{3}

Show Solution