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F.2 Maths(20points)
發問:
Factorize the following expressions. 1.3(a-b)(3r-t) + 9(b-a) 2.(m-n)^2 + n(n-m) 3.-ab(rx-s) - ab^2 (s-rx)^2 Simplify the following expressions. 4.(5ab-10a) / (15a) 5.5x / 6y divide by 15x / 2y 6.(2x) / {x(x-1)} plus (5) / (-3x) I don't know how to do, help me plz~
1.) 3(a-b)(3r-t) + 9(b-a) =3(a-b)(r-t)-9(a-b) =3(a-b)(r-t-9) 2.) (m-n)^2 + n(n-m) =(m-n)^2-n(m-n) =(m-n)(m-n-n) =(m-n)(m-2n) 3.) -ab(rx-s) - ab^2 (s-rx)^2 =ab(s-rx)-ab^2(s-rx)^2 =ab(s-rx)[1-b(s-rx)] =ab(s-rx)(1-bs+brx) 4.) (5ab-10a) / (15a) =5a(b-2)/15a =(b-2)/3 5.) 5x / 6y divide by 15x / 2y (5x / 6y)/(15x / 2y) =5x/6y*2y/15x =5x/15x*2y/6y =1/3*1/3 =1/9 6.) (2x) / {x(x-1)} plus (5) / (-3x) (2x) / {x(x-1)} * (5) / (-3x) =2/(x-1)*5/(-3x) =10/(x-1)(-3x) =10/3x(1-x) [=10/3x-3x^2]
其他解答:
1.)3(a-b)(r-t-9) 2.)(m-n)(m-2n) 3.)ab(s-rx)(1-bs+brx) 4.)(b-2)/3 5.)1/9 6.)[10/3x-3x^2] I think it is very good for you......|||||3(a-b)(3r-t-3) (m-n)(m-2n) ab(rx-s)(b-1) (b-2)/3 1/6 1/3x(1-3x) Wish this can help you|||||Factorize the following expressions 1. 3(a-b)(3r-t) + 9(b-a) = 3(a-b)(3r-t) - 9(a-b) = 3(a-b)(3r-t) - 3[3(a-b)] = 3(a-b) [3r-t-3] 2. (m-n)^2 + n(n-m) = (m-n)(m-n) - n(m-n) = (m-n) (m-n-n) = (m-n) (m-2n) 3. -ab(rx-s) - ab^2 (s-rx)^2 = ab(s-rx) - ab^2 (s-rx)(s-rx) = ab(s-rx) [1-b(s-rx)] Simplify the following expressions. 4. (5ab-10a) / (15a) = 5a(b-2) / 15a = (b-2) / 3 5. 5x / 6y divide by 15x / 2y = 5x / 6y x 2y / 15x = 1 / 9 6. (2x) / {x(x-1)} plus (5) / (-3x) = (2x) / [(x) (x-1)] - (5) / (3x) = [(2x) (3x)] / [(x) (x-1) (3x)] - [(5) (x) (x-1)] / [(3x) (x) (x-1)] = [6x^2] / [(x) (x-1) (3x)] - [(5x^2 - 5x)] / [(3x) (x) (x-1)] = [6x^2 - (5x^2 - 5x)] / [(3x) (x) (x-1)] = [x ^2 + 5x] / [(3x) (x) (x-1)] = [x (x+5)] / [(3x) (x) (x-1)] = [x + 5] / [(3x) (x-1)] 2007-09-13 21:57:35 補充： Factorize 的秘決: x - y = - (y x)Simplify 的秘決: 第4及第5題: 將分子及分母先factorize, 若分子及分母有些項目是一樣, 就可以除消第6題: 通分母, 再用第4及第5題的方法另外, 以下題目可以再簡單化3. ab(s-rx) [1-b(s-rx)] = ab(s-rx)[1-bs-brx]6. [x 5] / [(3x) (x-1)] = [x 5] / [3x^2-3x]|||||Key to solve 1 - 3: (a - b) = -(b - a) 1. 3(a - b)(3r - t) + 9(b - a) = 3(a - b)(3r - t) - 9(a - b) = 3(a - b) (3r - t - 3) 2. (m - n)2 + n(n - m) = (m - n)2 - n(m - n) = (m - n)(m - n - n) = (m - n)(m - 2n) 3. -ab(rx - s) - ab2 (s - rx)2 = -ab(rx - s) - ab2 (rx - s)2 Note: (a - b)2 = [ -(b - a)]2 = (b - a)2 = -ab(rx - s) [1 + ab(rx - s)] = -ab(rx - s) (1 + abrx - abs) Key to solve 4 - 6: Factorize the numerator first. Then cancel out like terms. 4. (5ab - 10a) / 15a = [5a(b - 2a)] / 15a = (b - 2a) / 3 5. (5x / 6y) / (15x / 2y) = (5x)(2y) / [ (6y)(15x) ] = 1/9 6. 2x / [ x(x - 1) ] + 5 / -3x = -6x / [ -3x(x - 1) ] + 5(x - 1)/ [ -3x(x - 1) ] = [5x(x - 1) - 6x ] / [ -3x(x - 1) ] = x(5x - 11) / [ -3x(x - 1) ] = (5x - 11) / [ -3(x - 1) ]|||||第1題: 3(a-b)(3r-t-3) 第2題: (m-n)(m-2n) 第3題: ab(rx-s)(b-1) 第4題: (b-2)/3 第5題: 1/6 第6題: 1/3x(1-3x) 應該幫到你|||||咁多條數百分開問先答你
F.2 Maths(20points)
發問:
Factorize the following expressions. 1.3(a-b)(3r-t) + 9(b-a) 2.(m-n)^2 + n(n-m) 3.-ab(rx-s) - ab^2 (s-rx)^2 Simplify the following expressions. 4.(5ab-10a) / (15a) 5.5x / 6y divide by 15x / 2y 6.(2x) / {x(x-1)} plus (5) / (-3x) I don't know how to do, help me plz~
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最佳解答:1.) 3(a-b)(3r-t) + 9(b-a) =3(a-b)(r-t)-9(a-b) =3(a-b)(r-t-9) 2.) (m-n)^2 + n(n-m) =(m-n)^2-n(m-n) =(m-n)(m-n-n) =(m-n)(m-2n) 3.) -ab(rx-s) - ab^2 (s-rx)^2 =ab(s-rx)-ab^2(s-rx)^2 =ab(s-rx)[1-b(s-rx)] =ab(s-rx)(1-bs+brx) 4.) (5ab-10a) / (15a) =5a(b-2)/15a =(b-2)/3 5.) 5x / 6y divide by 15x / 2y (5x / 6y)/(15x / 2y) =5x/6y*2y/15x =5x/15x*2y/6y =1/3*1/3 =1/9 6.) (2x) / {x(x-1)} plus (5) / (-3x) (2x) / {x(x-1)} * (5) / (-3x) =2/(x-1)*5/(-3x) =10/(x-1)(-3x) =10/3x(1-x) [=10/3x-3x^2]
其他解答:
1.)3(a-b)(r-t-9) 2.)(m-n)(m-2n) 3.)ab(s-rx)(1-bs+brx) 4.)(b-2)/3 5.)1/9 6.)[10/3x-3x^2] I think it is very good for you......|||||3(a-b)(3r-t-3) (m-n)(m-2n) ab(rx-s)(b-1) (b-2)/3 1/6 1/3x(1-3x) Wish this can help you|||||Factorize the following expressions 1. 3(a-b)(3r-t) + 9(b-a) = 3(a-b)(3r-t) - 9(a-b) = 3(a-b)(3r-t) - 3[3(a-b)] = 3(a-b) [3r-t-3] 2. (m-n)^2 + n(n-m) = (m-n)(m-n) - n(m-n) = (m-n) (m-n-n) = (m-n) (m-2n) 3. -ab(rx-s) - ab^2 (s-rx)^2 = ab(s-rx) - ab^2 (s-rx)(s-rx) = ab(s-rx) [1-b(s-rx)] Simplify the following expressions. 4. (5ab-10a) / (15a) = 5a(b-2) / 15a = (b-2) / 3 5. 5x / 6y divide by 15x / 2y = 5x / 6y x 2y / 15x = 1 / 9 6. (2x) / {x(x-1)} plus (5) / (-3x) = (2x) / [(x) (x-1)] - (5) / (3x) = [(2x) (3x)] / [(x) (x-1) (3x)] - [(5) (x) (x-1)] / [(3x) (x) (x-1)] = [6x^2] / [(x) (x-1) (3x)] - [(5x^2 - 5x)] / [(3x) (x) (x-1)] = [6x^2 - (5x^2 - 5x)] / [(3x) (x) (x-1)] = [x ^2 + 5x] / [(3x) (x) (x-1)] = [x (x+5)] / [(3x) (x) (x-1)] = [x + 5] / [(3x) (x-1)] 2007-09-13 21:57:35 補充： Factorize 的秘決: x - y = - (y x)Simplify 的秘決: 第4及第5題: 將分子及分母先factorize, 若分子及分母有些項目是一樣, 就可以除消第6題: 通分母, 再用第4及第5題的方法另外, 以下題目可以再簡單化3. ab(s-rx) [1-b(s-rx)] = ab(s-rx)[1-bs-brx]6. [x 5] / [(3x) (x-1)] = [x 5] / [3x^2-3x]|||||Key to solve 1 - 3: (a - b) = -(b - a) 1. 3(a - b)(3r - t) + 9(b - a) = 3(a - b)(3r - t) - 9(a - b) = 3(a - b) (3r - t - 3) 2. (m - n)2 + n(n - m) = (m - n)2 - n(m - n) = (m - n)(m - n - n) = (m - n)(m - 2n) 3. -ab(rx - s) - ab2 (s - rx)2 = -ab(rx - s) - ab2 (rx - s)2 Note: (a - b)2 = [ -(b - a)]2 = (b - a)2 = -ab(rx - s) [1 + ab(rx - s)] = -ab(rx - s) (1 + abrx - abs) Key to solve 4 - 6: Factorize the numerator first. Then cancel out like terms. 4. (5ab - 10a) / 15a = [5a(b - 2a)] / 15a = (b - 2a) / 3 5. (5x / 6y) / (15x / 2y) = (5x)(2y) / [ (6y)(15x) ] = 1/9 6. 2x / [ x(x - 1) ] + 5 / -3x = -6x / [ -3x(x - 1) ] + 5(x - 1)/ [ -3x(x - 1) ] = [5x(x - 1) - 6x ] / [ -3x(x - 1) ] = x(5x - 11) / [ -3x(x - 1) ] = (5x - 11) / [ -3(x - 1) ]|||||第1題: 3(a-b)(3r-t-3) 第2題: (m-n)(m-2n) 第3題: ab(rx-s)(b-1) 第4題: (b-2)/3 第5題: 1/6 第6題: 1/3x(1-3x) 應該幫到你|||||咁多條數百分開問先答你
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