How can a^2 - 36b^2 be factorized?The expression given is a squared - 36 b squared
Remember that a^2 - 36b^2 is the same as a^2 + 0ab - 36b^2.
Then factor like any such polynomial:
(a + __) (a - __) -- a being the square root of a^2. Also, the negative sign before the third term tells you the signs are different (+ and -).
(a + 6b) (a - 6b) -- 6b being the square root of 36b^2. Since 6ab and -6ab cancel each other out, there is no need to figure out which one is positive and which negative.
The expression to be factorized "asquared - 36bsquared" can be written more appropriately as a^2 - 36*b^2
a^2 - 36*b^2
=> a^2 - (6b)^2
use the relation x^2 - y^2 = (x + y)(x - y)
=> (a - 6b)(a + 6b)
This gives the factorized form of a^2 - 36*b^2 = (a - 6b)(a + 6b)
a^2 - 36b^2
this is an example of the pattern called "Difference of Squares"
the rule for "Difference of Squares" is x^2 - y^2 = (x + y)(x - y)
a^2 - 36b^2 = (a + 6b)(a - 6b)
you can use FOIL to check this.