How do you factor 4b^2 - 94b2−9?

1 Answer
sente
Nov 14, 2015

4b^2 - 9 = (2b + 3)(2b-3)4b2−9=(2b+3)(2b−3)

Explanation:

The difference of squares formula states that
a^2 - b^2 = (a+b)(a-b)a2−b2=(a+b)(a−b)
(this may be easily verified by expanding the right hand side of the equation)

4b^2 = (2b)^24b2=(2b)2
9 = 3^29=32

Thus, by the difference of squares formula:

4b^2 - 9 = (2b)^2 - 3^2 = (2b + 3)(2b-3)4b2−9=(2b)2−32=(2b+3)(2b−3)

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