Algebra: Chapter 6, Lesson 2, page 266
Difference of 2 squares
For a binomial to be a difference of 2 squares, 2 conditions must be met.
- There must be 2 terms, both must be square (e.g., `4x^2` and `9x^4`)
There must be a minus sign `(-)` between the 2 terms.
We are going backward in our factoring, using our first Chapter 5 shortcut formula:
`a^2 – b^2 = (a + b)(a – b)`,
so once we have the 2 squares, just plug them in to our formula!
Examples:
`9a^8b^4 – 49 = (3a^4b^2)^2 – 7^2`
`= (3a^4b^2 + 7)(3a^4b^2 – 7)`
and another example where we have to factor something out first, namely `x^4`, we have:
`49x^4 – 9x^6 = x^4(49 – 9x^2) `
`= x^4[7^2 – (3x)^2]`
with the final factors being = `x^4(7 +3x)(7 – 3x)`