Question

(ax + b) × (cx + d) =

Answer 1

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.

Answer 2

A * c *$x^{2}$  +  a * x *d  +  b * c* x  +  b * d  = ac$x^{2}$ + ( ad + bc)x + bd.