when multiplying polynomials, is there a specific order you should use in multiplying each term ?

Question

vertical format to multiply (2x + 3) by (5x+4)

5x + 4   OR  2x + 3

2x + 3           5x+4

 

Our text book instructions and answer key show all calculations using the second set of numbers first (the first example I've shown).  It does not give a reason for this. 

thank you

Answer 1

In arithmetic or algebraic multiplication the order of the multiplicands is unimportant because a×b=b×a, where a and b are any numerical or algebraic expressions. This is the commutative property which applies to arithmetic and algebraic multiplication and addition, but not to division and subtraction.