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5-2-79 difference of functions
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    When doing this kind of problem, we actually need to understand what it's asking first. So I frequently will ask students to think about if it was a number. If I asked you for F of one, you hopefully would tell me we put one in every time we see the unknown and we would get 5. That's actually a point, the .15. Or if I said what's F of two, you would then put two in every time you see the unknown. So you would get 8. So that's the .28. So in the first one, it wants to know what is F of T - 5 S Every time I see the unknown, I'm going to put in t - 5 S T - 5 ^2 + 4. I'm going to foil that out. T - 5 * T - 5 + 4. So first outer inner last t ^2 - 5 T minus five T + 25 + 4. So our final answer, t ^2 - 10 T plus 29. That was part A Part B wants F of W + H -, F of W, so F of W + H Every time I see the unknown, I'm going to put in W + H, so W + H ^2 + 4. We're going to foil that out. W + H * W + H + 4, so W ^2 plus WH plus WH plus H ^2 + 4. So this whole thing is just W ^2 + 2 WH plus H ^2 + 4. Now there's a second part to that. It says we then want to subtract F of West. Well, F of West would just be W ^2 + 4. So when we put this whole thing together, the F of W + H -, F of West. So we'd have W ^2 + 2, WH plus H ^2 + 4. That whole thing subtracted W ^2 + 4. When we distribute that negative sign, we can see the W squareds and the fours are going to cancel. So we would get W2 WH plus H ^2 to be what's left for the last one. It's going to be the same kinds of steps. We'd have the FW which we already had, and we're going to subtract FW minus H Well, F of W -, H Once again, every time I see the unknown, I'm putting in whatever was in the parentheses. If we foil this out, we can see we'd get W ^2 -, 2 WH plus H ^2 + 4. So for this one, I'm running out of room. I'm going to come and put it up here. We would have the FW which was W ^2 + 4 minus the WFW minus H So add W ^2 -, 2 WH plus H ^2 + 4. When we simplify that, the W squareds and the fours are going to cancel. So we would end up distributing that negative. We'd get 2 WH minus H ^2.