Question

Evaluate : (a+b) (a-b)​

Answer 1

To solve this problem, you will want to FOIL.

That is, multiply the Firsts (the left-most terms in each parentheses (the 1st term in the 1st parentheses by the 1st term in the 2nd parentheses)),

Then, multiply the Outers (the terms on the far left and right (the 1st term in the 1st parentheses by the 2nd term of the 2nd parentheses)),

Then, multiply the Inners (the two terms closest to the center (that is, the 2nd term of the 1st parentheses by the 1st term of the 2nd parentheses)),

Finally, multiply the Lasts (the right-most terms in each parentheses (the 2nd term of the 1st parentheses by the 2nd term of the 2nd parentheses)).

(Firsts, Outers, Inners, Lasts → F.O.I.L.)

Now, apply it!

(A + B) (A - B) → Firsts: A * A = A^2 (A squared) → Outers: A * (-B) = (-AB) → Inners: B * A = AB → Lasts: B * (-B) = (-B^2)

Now, add the products together:

A^2 + (-AB) + AB + (-B^2) =

A^2 - AB + AB - B^2 → Like terms AB cancel to get your final answer →

A^2 - B^2.

Hope that helps!

(P.S. This type of problem is called a Difference of Squares, as the solution is one perfect square (A^2) minus another (B^2)).