Multiply every term of the first polynomial by every term of the
second polynomial and then collect like terms if possible.

Here is a illustration of what you do in general:

(A + B + C + D + E)(F + G + H) =

AF + AG + AH + BF + BG + BH + CF + CG + CH + DF + DG + DH

Note that there are 5 terms in the first and 3 terms in the second,
so therefore there are 5×3 or 15 terms.  Of course none of these are
like terms, but normally some are.

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Your last problem:

(2x-5)(4x2-3x+1)

The first polynomial has 2 terms, the second polynomial has 3 terms,
So there will be 2×3 or 6 terms before you combine terms.  So we multiple
every term of the first by every term of the second:

(2x)(4x2) + (2x)(-3x) + (2x)(1) + (-5)(4x2) + (-5)(-3x) + (-5)(1)

Simplify

8x3 - 6x2 + 2x - 20x2 + 15x - 5

Combine the two pairs of like terms:

8x3 - 26x2 + 17x - 5

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Suppose you had

(3y3-2y2+7y-5)(2y2-y+9)

The first polynomial has 4 terms, the second polynomial has 3 terms,
So there will be 4×3 or 12 terms before you combine terms.  So we multiply
every term of the first by every term of the second.
(I'll have to write them small to get all 12 on one line):


(3y3)(2y2)+(3y3)(-y)+(3y3)(9)+(-2y2)(2y2)+(-2y)(-y)+(-2y)(9)+(7y)(2y2)+(7y)(-y)+ (7y)(9)+(-5)(2y2)+(-5)(-y)+(-5)(9)

Simplify:


6y5 - 3y4 + 27y3 - 4y4 + 2y3 - 18y2 + 14y3 - 7y2 + 63y - 10y2 + 5y - 45

Combine all the like terms:

6y5 - 7y4 + 43y3 - 35y2 + 68y - 45

Edwin