Question

(ax + b) × (cx + d) =

Answer 1

a * c *
`x^(2)` + a * x *d + b * c* x + b * d = ac
`x^(2)` + ( ad + bc)x + bd.

Answer 2

These are easy if you know " FOIL ". That's a procedure that takes you through multiplying two binomials.

FOIL stands for
-- First terms
-- Outside terms
-- Inside terms
-- Last terms

and that's how you keep everything straight while you're doing it.

(ax + b) x (cx + d)

Multiply First terms . . . 'ax' times 'cx' = acx²

Multiply Outside terms . . . 'ax' times 'd' = adx

Multiply Inside terms . . . 'b' times 'cx' = bcx

Multiply Last terms . . . 'b' times 'd' = bd

Now addummup:

(ax + b) x (cx + d) = acx² + adx + bcx + bd

From there, you can look for opportunities to make it look cleaner and prettier ... factoring, combining like terms, etc.