Hey what is the pattern for areas of rectangles?

Question

(explain the distributive property)

Area: (2x +1) ( x+3) = 2x + 7x + 3
which is: length: 2 + 1 width: + 3

What's the pattern that would work with all of them?other random ones?

(PS: this is grade 8 stuff...)

Answer 1

Length:
2x + 1

Width:
x + 3

Area:
(2x + 1)(x + 3) = 2x² + 7x + 3

Or in general:

Length:
ax + b

Width:
cx + d

Area (ax + b)(cx + d)

Multiply using FOIL:

First:
ax * cx = ac(x²)

Outer:
ax * d = ad(x)

Inner:
bx * c = bc(x)

Last:
c * d = cd

All together:

(ac)x² + (ad + bc)x + cd