w^2-16w+48

Question

using the foil method, explain your work

Answer 1

To expand the expression w^2-16w+48 using the FOIL method, we first need to find two numbers that multiply to 48 (the last term) and add up to -16 (the middle term).

The two numbers that satisfy these conditions are -4 and -12, because -4 * -12 = 48 and -4 + (-12) = -16.

Now we can rewrite the middle term -16w as -4w-12w.

So the expression w^2-16w+48 can be written as:

w^2 - 4w - 12w + 48

Now we can apply the FOIL method to multiply the terms:

(w-4)(w-12)
= w*w + w*(-12) + (-4)*w + (-4)*(-12)
= w^2 -12w - 4w + 48
= w^2 - 16w + 48

So, w^2-16w+48 expanded using the FOIL method is equal to (w-4)(w-12).