<— Unit 3: Part 4 —>
Polynomials
Sum & Difference of Squares
Sum & Difference of Cubes
Factor Polynomial
Page 8

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<— Unit 3: Part 4 —>
Polynomials
Sum & Difference of Squares
Sum & Difference of Cubes
Factor Polynomial
Page 8

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Difference of Squares
Work I would probably show under the cut!
Can you Help my Builder?
He’s been asked to quote for a patio by an eccentric mathematics professor. The client is providing 112 square slabs, each side being 18 inches long. [Note for continental readers: there are 12 inches in one foot, which is about 30cm.]
The patio itself must be square and enclose a square unpaved area for a tree. Also all of the slabs must be used. My builder has thought of a patio 29 slabs by 29 with an enclosed unpaved area of 27 x 27, but, as well as being impractical, it would be 43.5 feet wide and the garden is only 22 feet wide.
Can you find a suitable layout which would fit the professor’s garden? The answer will appear here in a few days.
(22/06/2018)
Answer added on 24/06/2018: The patio is 11 x 11 slabs and the enclosed unpaved area is 3 x 3. Thus (11 x 11) - (3 x 3) = 121 - 9 = 112.
So if one person ignores you and the other doesn't, is that difference of cares.

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what is the simplified factored form of x^4-81?
Anywho! Radicals, needing a little help with multiplying and conjugates.(3√x +4)(3√x-4) [3's indicate cube roots]
Ah okay. So this is like multiplying out the more traditional form of (x-a)(x-a), where x in this case is and a is 4. So in the generic case, we see that it multiplies out to . Here, it's the same idea and the answer will be . This is the same as: .
Hope this helps!
-Aet
Today there was a question on how to factor the difference of squares. This video provides a quick brush-up on the skill.