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This method is easier than the long multiplication of 999x999

Binomial Expansion – Reflection. Introduction My task is to find the application of the general rule for expanding binomials in particular squaring the sum and difference of two terms. (a+b) 2 =a 2 +2ab+b 2 and (a-b) 2 =a 2 -2ab+b 2 Q1

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This method is easier than the long multiplication of 999x999

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  1. Binomial Expansion – Reflection. Introduction My task is to find the application of the general rule for expanding binomials in particular squaring the sum and difference of two terms. (a+b)2=a2+2ab+b2 and (a-b)2=a2-2ab+b2 Q1 In olden days when there was no calculator, long multiplication was taking much time. To find the product of two same numbers this general rule for expanding binomials can be made use. This method was much easier than the long multiplication. For example to find the area of square field of side 999m. Area = (999)2 =(1000-1)2 =10002-2(1000)(1)+12 =1000000-2000+1 =998001m2 This method is easier than the long multiplication of 999x999

  2. Q2 This general rule for expanding binomials helps us to find the product of two larger numbers which can be expressed as the sum or difference of the multiples of 10,100,1000..etc very easily in comparison with the long multiplication. Also when the numbers are decimals which can be expressed as the sum or difference of 1 and 0.1, 0.01,0.001…..etc. E.G 1 0.9992=(1-0.001)2= a2-2ab+b2 =1-2(1) (0.001) + (0.001)2 =1-0.002+0.000001 =1.000001-0.002 =0.998001 E.G 2 0.986472 =(1-0.01353)2 =12-2(1)(0.01353)+0.01353)2 =1-0.02706+0.0001830609 =0.973123060 This expansion method will not be easy to solve out the answer. So we would prefer to use long multiplication rather than choosing the expansion method. EG.3 839422=(80000+3942)2 =800002+2(80000)(3942)+39422 =6400000000+(160000)(3942)+(3942)2 =6400000000+(16)(3942)x10000+(3942)2 +6400000000+630720000+15539364 =7046259364 For this multiplication the expansion method is not easy.

  3. Q3 If the numbers are very large which can not be expressed as the sum or difference of the multiples of 10,100,1000……etc this method will not be easy in comparison with the long multiplication method. To find the area of a rectangle field of length 553m and 485m, area=553x485m2. In this one we can not use the general rule for expanding binomials. So long multiplication is more efficient than the expansion method. Generally this expansion method is easy to find the product of two numbers only if both numbers are the same or to find the square of a number otherwise long multiplication method is more efficient than the expansion method. EG1 To find the product of 6479 and 3947 we can not use the expansion method so long multiplication is preferable . 6479x3947 =25572613 EG2 837962=83796x83796 83796=80.000+3000+700+90+6 Therefore 8379x83796 =83796x(80,000+3000+700+90+6) 837962 by method of long multiplication. =83796x6=502,776 +83796x90=7,541,640 +83796x700=58,657,200 +83796x3000=251,388,000 +83796x80000=6,703,680,000 =7,021,769,616 In this case long multiplication is easier than binomial expansion method.

  4. Done By: Ghada Ahmed Al Kuwari Class:8B Date submitted: Tuesday,November,2,2010

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