Question

6. Find the product for both sets of polynomials below by multiplying vertically.

A.4x2 - 4x
x*x² - 4
————

B)
x²+x-2
*4x² - 8x
———-

Answer 1

A)
`4x^5-4x^4-16x^2+16x`

B)
`4x^4-4x^3-16x^2+16x`

Also, maybe that vertically means:

A)
`4x^2 \cdot x^3` and
`(-4x) \cdot (-4)`

Resulting in
`4x^5+16x`

B)
`x^2 \cdot 4x^2` and
`x \cdot (-8x)` and
`-2 \cdot 0`

Resulting in
`4x^4-8x^2`

Explanation:

It seems that you want to multiply the polynomials in this way:
`(\text{Polynomial - 1})\cdot(\text{Polynomial - 2})`

A)

`4x^2-4x`

`x \cdot x^2 -4`

`(4x^2-4x)(x \cdot x^2 -4)=(4x^2-4x)(x^3 -4)`

`(4x^2-4x)(x^3 -4)\\`

`4x^5-16x^2-4x^4+16x`

`4x^5-4x^4-16x^2+16x`

B)

`x^2+x-2`

`4x^2-8x`

`(x^2+x-2)(4x^2-8x)`

`4x^4-8x^3+4x^3-8x^2-8x^2+16x`

`4x^4-4x^3-16x^2+16x`