How can a^2 - 36b^2 be factorized?The expression given is a squared - 36 b squared

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samhouston's profile pic

samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted on

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.

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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)

rugbykats's profile pic

rugbykats | High School Teacher | (Level 2) Adjunct Educator

Posted on

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.

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