Let's begin by recalling the formula to square the sum of two monomials.
( a+ b)^2 = a^2 + 2 a b + b^2
Thus, to square a sum of two quantities, we add the square of the first quantity plus twice the product of the two quantities plus the square of the second quantity. Next, let's recall the formula to square the difference of two monomials.
( a- b)^2 = a^2 - 2 a b + b^2
From the above, to square a difference of two quantities, we add the square of the first quantity minus twice the product of the two quantities plus the square of the second quantity. Finally, let's recall the formula to multiply a sum and a difference.
( a+ b)( a- b) = a^2 - b^2
To find the product of a sum of two quantities and a difference of the same two quantities, we add the square of the first quantity minus the square of the second quantity.
