Whats different in FOIL method and distributive property method?

Question

What is the relationship between the FOIL method for multiplying polynomials and the distributive property of multiplication?

Answer 1

FOIL deals with the products of the first (F) terms of the binomial factors.

Then we take the product of the outer (O) terms (the first term of the first factor and the second term of the second factor).

Then we take the product of the inner (I) terms (the second term of the first factor and the first term of the second factor).

Finally we take the product of the last (L) terms (the second term of each factor).

We add these products together.

The distributive method gives the same result but the multiplication is different. We take the first term of the first factor and distribute it by multiplying it by each of the terms in the second factor. We get two products this way and we add them together. Then we add the sum of the product of the second term of the first factor with each of the terms of the second factor.

EXAMPLE

FOIL method

(ax+b)(cx+d)=(ax)(cx) + (ax)(d) + (b)(cx) + (b)(d)=acx²+(ad+bc)x+bd.

Distributive method

(ax+b)(cx+d)=ax(cx+d)+b(cx+d)=acx²+adx+bcx+bd=acx²+(ad+bc)x+bd.