Algebra: Chapter 5, Lesson 10, page 245.
Multiplying Binomials: Special Products
We can use the FOIL or BOX methods to multiply binomials. There are however, 3 special cases that if you recognize them, will save you some work:
- `(A+B)(A-B)=A^2−B^2`
- `(A+B)(A+B)=A^2+B^2+2AB`
- `(A−B)(A−B)=A^2+B^2−2AB`
Remember, that `A` and `B` are the terms (monomials or constants) that we just plug in. If you forget these 3 cases, that’s OK, just FOIL or BOX the binomials and the answers are still the same.
For example:
`(2x + 7)(2x – 7)` where `2x = a` and `7 = b`, we have an answer of `4x^2 – 49`.
Another example:
`(2x + 7)(2x +7)` where again `2x = a` and `7 = b`, we have an answer of `4x^2 + 49 + 2*2x*7` or `4x^2 +28x + 49`!
Go slow and you’ll be fine.