Theory:

To multiply a trinomial by a trinomial, you need to multiply each term of one trinomial by each terms of another trinomial and add the resulting products.
 
a+b+cd+e+f==ad+ae+af+bd+be+bf+cd+ce+cf=ad+ae+af+bd+be+bf+cd+ce+cf
When degrees are multiplied with the same bases, their indicators add up.
 
aman=am+n
Example:
7+b+c4a5+2ab+c2=74a5+72ab+7c2+b4a5+b2ab+bc2+c4a5+c2ab+cc2=28a5+14ab+7c2+4a5b+2ab2+bc2+4ca5+2abc+c3
 
 
5xy3x2+zx2+y+1==5xyx2+5xyy+5xy13x2x23x2y3x21+zx2+zy+z1=5x1+2y+5xy1+1+5xy3x2+23x2y3x2+zx2+zy+z=5x3y+5xy2+5xy3x43x2y3x2+zx2+zy+z
 
Pay attention to the signs! 
 
5x2yx+t22x2y+t==5x2y2x2+5x2yy+5x2ytx2x2xyxt+t22x2+t2(y)+t2t=52x2+2y5x2y1+1+5x2yt2x2+1+xyxt+2x2t2t2y+t2+1=10x4y5x2y2+5x2yt2x3+xyxt+2x2t2t2y+t3