Question

How do you find `a=(3b+c)+5b` given `b=<6,3>` and `c=<-4,8>`?

Answer 1

`a= < 44, 32 >`

Explanation:

We can simplify the given `color(red)(a)=(3color(blue)(b)+color(green)(c))+5color(blue)(b)` a bit as:
`color(white)("XXX")color(red)(a)=8color(blue)(b)+color(green)(c)`

Given that `color(blue)(b)=color(blue)(< 6,3>)`
then
`color(white)("XXX")color(blue)(8b)=< 6*8,3*8 > = color(blue)(< 48,24>)`

and given that `color(green)(c)=color(green)( < -4, 8 >`

we have
`color(white)("XXX")color(red)(a)=color(blue)(< 48, 24 >) + color(green)( < -4,8 >)`

`color(white)("XXXX")= < color(blue)48color(green)(-4), color(blue)(24)color(green)(+8) >`

`color(white)("XXXX")= < 44, 32 >`