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Q: What is the highest common factor of 12ab and 4a2b?

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The LCM of 4a2b and 6a10b is 12a10b

The GCF is 4a2b The LCM is 12a3b2

(x + y)2 = x2 + 2xy + y2 So x2 + y2 = (x + y)2 - 2xy = a2 - 2b Then (x2 + y2)2 = x4 + 2x2y2 + y4 So x4 + y4 = (x2 + y2)2 - 2x2y2 = (a2 - 2b)2 - 2b2 = a4 - 4a2b + 4b2 - 2b2 = a4 - 4a2b + 2b2

Your notation is confusing. It looks like: 8a3 + 4a2b - 2ab2 - b3. So if you look at it, notice 23 = 8 & 22 = 4, so take c = (2*a), and you have c3 + c2b - cb2 - b3, Now note that if c = b, the polynomial is zero, so (c-b) or (b-c) is a factor. So divide by (c-b) using long division: (c - b)(c2 + 2cb + b2) {the second polynomial is a perfect square: (c+b)2}, so (c-b)(c+b)2, then substitute c = 2a, and get (2a-b)(2a+b)2 finally, multiply it out to make sure you get the original polynomial.

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