Question

Hello. Please help clarify problem 4 and 5. Thank you

Answer 1

Distribute and simplify the following:

`\begin{gathered} (5-i)(2+4i) \\ (3-x+2x^2+4x^3)(4x-5) \end{gathered}`

To distribute is to open the bracket:

`\begin{gathered} (5-i)(2+4i) \\ 10+4i-2i-4i^2 \\ 10+2i-4i^2 \\ \text{where i}^2=-1 \\ 10+2i-4(-1) \\ 10+2i+4 \\ \text{collect like terms} \\ 14+2i \end{gathered}`

(b)

`\begin{gathered} (3-x+2x^2+4x^3)(4x-5) \\ 4x(3-x+2x^2+4x^3)-5(3-x+2x^2+4x^3) \\ 12x-4x^2+8x^3+16x^4-15+5x-10x^2-10x^3 \\ collect\text{ like terms} \\ 16x^4+8x^3-10x^3-4x^2-10x^2+12x+5x-15 \\ 16x^4-2x^3-14x^2+17x-15 \end{gathered}`