The area can be figured as the difference of the enclosing rectangle area ((3x-2)×(4x-1)) and the area of the white space at the lower left (horizontal dimension x+1).
The vertical dimension of the white space at lower left is The difference of the given vertical dimensions:
The product of any polynomial with any other can be found using the distributive property repeatedly. When both polynomials are binomials, a mnemonic can help you make sure all product terms are included.
(a +b)(c +d) = a(c +d) + b(c +d) . . . . use the distributive property to eliminate the first set of parentheses
= ac +ad +bc +bd . . . . . . . . . . . . . . use the distributive property to eliminate remaining parentheses
You will notice that the final product is the sum of the terms ...
ac . . . product of First terms of the binomials
ad . . . product of Outer terms of the expression
bc . . . product of Inner terms of the expression
bd . . . product of Last terms of the binomials
The letters of these descriptive words form the mnemonic FOIL, which is sometimes used as a verb (as above: FOIL each product).
