Answer :
a * c *[tex] x^{2} [/tex] + a * x *d + b * c* x + b * d = ac[tex] x^{2} [/tex] + ( ad + bc)x + bd.
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.
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.
