Some two termed quadratic expressions are in the form of difference of two squares. For example:
x2 - 25 can be written as x2 - 52 because 52 equals 25
Some more examples:
- x2 - 36 = x2 - 62
- 9x2 - 81 = (3x)2 - 92
- 25x2 - 36y2 = (5x)2 - (6y)2
These quadratic expressions can be factored by applying the formula for difference of two squares:
For example, the quadratic expression x2 - 36 can be written as x2 - 62.
x2 - 62 can be compared to a2 - b2 in the above mentioned formula, hence you get
For example, the algebraic expression (x + 2)(x - 2) can be expanded by distribution as follows:
(a2 - b2) = (a + b)(a - b)Working forward with the formula - Factorization
For example, the quadratic expression x2 - 36 can be written as x2 - 62.
x2 - 62 can be compared to a2 - b2 in the above mentioned formula, hence you get
x2 - 36 = x2 - 62 = (x + 6)(x - 6)Working backward with the formula - Expansion
For example, the algebraic expression (x + 2)(x - 2) can be expanded by distribution as follows:
`(x + 2)(x - 2) = x^2 + 2x - 2x - 4 = x^2 - 4`.. which is the same result as obtained when applying the above formula backwards:
`(x + 2)(x - 2) = x^2 - 2^2 = x^2 - 4`
