Question

What is the standard form of a polynomial `(5h + 4)(3h + 6)`?

Answer 1

`(5h+4)(3h+6)=15h^2+42h+24`

Explanation:

`(5h+4)(3h+6)=5h(3h+6)+4(3h+6)`
`=5hxx3h+5hxx6+4xx3h+4xx6`
`=5xx3xxhxxh+5xx6xxh+4xx3xxh+4xx6`
`5xx3=15`
`hxxh=h^2`
`5xx3xxhxxh=15h^2`
`5xx6=30`
`5xx6xxh=30h`
`4xx3=12`
`4xx3xxh=12h`
`4xx6=24`
`5xx3xxhxxh+5xx6xxh+4xx3xxh+4xx6`
`=15h^2+30h+12h+24`
`30h+12h=42h`
`15h^2+30h+12h+24=15h^2+42h+24`
Thus,
`(5h+4)(3h+6)=15h^2+42h+24`