Question 441725
This is an example of a quadratic that you manually have to write in the middle variable. From there, you just Un-FOIL as usual. The LONG way follows:

1.) {{{9x^2 - 49}}}
- This is the base equation. Note that you cannot factor out 3 or 9 due to the fact that 49 is not divisible by 3 (4 + 9 = 13 which is not divisible by 3). 

2.) {{{9x^2 + 0x - 49}}}
- This is the equation written in standard quadratic form. Note that the coefficient is zero.

3.) {{{9x^2 + 21x - 21x - 49}}}
- When unfoiling a standard quadratic (ax^2 + bx + c), you multiply a * c, then find two factors of the product that when added, make b. In this case it was 21 * (-21).

4.) {{{(9x^2 + 21x) - (21x - 49) = 3x(3x + 7) - 7(3x +7)}}}
- Here you factor out the GCF of each pair of terms.

5.) {{{(3x - 7)(3x + 7)}}}
- Finally, you factor out the common binomial factors. This is the answer.

The short way:

1.) {{{9x^2 - 49}}}
- This quadratic is an example of what is known as a "difference of squares" meaning that it's a term squared minus another term squared or {{{a^2 - b^2}}}. Note that there is no middle term as in a standard quadratic formula. 

2.) {{{(a - b)(a + b)}}}
- This is the factored form a difference of squares will always take once factored.

3.) a = (√9x^2) = 3x, b =(√49) = 7
- Find the root of both terms.

4.) {{{(3x - 7)(3x + 7)}}}
- Input values.