PDF Version of module - the Australian Mathematical Sciences ...
PDF Version of module - the Australian Mathematical Sciences ...
PDF Version of module - the Australian Mathematical Sciences ...
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The Improving Ma<strong>the</strong>matics Education in Schools (TIMES) Project{9}EXAMPLEExpand and simplify (2 5 – 3 2)(2 5 + 3 2).SOLUTION(2 5 – 3 2)(2 5 + 3 2) = (2 5) 2 – (3 2) 2 = 20 – 18 = 2.Notice in <strong>the</strong> above example, since we are taking a difference <strong>of</strong> squares, <strong>the</strong> answer turnsout to be an integer. We will exploit this idea in <strong>the</strong> next section.EXERCISE 3Caculate (5 3 + 7 2)(5 3 – 7 2).SQUARESIn addition to <strong>the</strong> important difference <strong>of</strong> two squares mentioned above, we also have <strong>the</strong>algebraic identities:(a + b) 2 = a 2 + 2ab + b 2 and (a – b) 2 = a 2 – 2ab + b 2 ,that also, <strong>of</strong> course, apply to surds.EXAMPLEExpand and simplifya (5 2 + 3 3) 2 b (3 2 – 10) 2SOLUTIONa (5 2 + 3 3) 2 = 25 4 + 9 9 + 30 6 = 77 + 30 6.b (3 2 – 10) 2 = 9 4 + 10 – 6 20 = 28 – 12 5.EXERCISE 4Suppose x and y are positive number, show that x × y = x + y + 2 xy and hencesimplify 11 + 2 30.
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