How do you factor the following polynomials?

Question

How do you factor these polynomial expressions? I am using this to study for an exam, so please explain how the answer is found in multiple steps.

36x^2 - 60x + 25 - y^2

a^4 - 2a^3 - a^3b + 2a^2b

Note: In the second problem, the exponents do not include the variable, they are written right after the term. The exponents are only the single constant number.

Anonym · Accepted Answer

A big part of math is pattern recognition. A lot of homework is just fighting with stuff so you will remember the pattern when you see it again. The most common pattern is (x + a) * (x + b) = x^2 + (a + b)x + ab and the special case (x + a) * (x - a) = x^2 - a^2. When you spot the pattern you can just write the answer from memory.

36x^2 - 60x + 25 - y^2

First we notice that we might have the difference of two squares. The power is 2 so we are looking for two factors of the form (ax + b)(cx + d). the root of 36 is 6 and the root of 25 is 5 and twice the sum of those is 60 so we have it nailed.

(6x - 5 - y)(6x - 5 + y)

jcherry_99 · Answer

36x^2 - 60x + 25 = (6x - 5)^2

(6x - 5) - y^2 = 
(6x - 5 - y)(6x - 5 + y)

Problem 2
a^3(a - 2) - a^2b(a - 2)
(a - 2)(a^3 - a^2b)
(a - 2) * a^2(a - b)

a^2(a - 2)(a - b)

How do you factor the following polynomials?

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