Вправи: 124

124. Спростіть вираз:

1) 4ba2- b2 + a-ba2+ ab + a+bb2- ab = 4b\aba-b(a+b) + a- b\b(a-b)a(a+b) – a+ b\a(a+b)b(a-b) = 4ab2+ b(a-b)2- a(a+b)2aba-b(a+b) = 4ab2+ ba2- 2ab+ b2- a(a2+ 2ab+ b2)aba-b(a+b) = 4ab2+ a2b-2ab2+ b3- a3- 2a2b-ab2aba-b(a+b) = ab2- a2b+ b3- a3aba-b(a+b) = abb-a+ (b-a)(b2+ ab+ a2)aba-b(a+b) = b-a(ab+ b2+ ab+ a2)aba-b(a+b) = a-b(a+b)2aba-b(a+ b) = a+bab;

2) 1x-2 + 1x+2 – xx2- 4 + x2+ 48x-2x3 = 1\2x(x+2)x-2 + 1\2x(x-2)x+2 – x\2xx-2(x+2) + x2+ 4-12x(4- x2) = 2xx+2+ 2xx-2- 2x2- (x2+ 4)2xx-2(x+2) = x2- 42x(x2- 4) = 12x;

3) 1(a-5b)2 – 2a2- 25b2 + 1(a+5b)2 = 1(a+5b)2(a-5b)2 – 2(a-5b)(a+5b)a-5b(a+5b) + 1(a-5b)2(a+5b)2= (a+5b)2- 2a-5ba+5b+ (a-5b)2(a+5b)2(a-5b)2 = a2+ 10ab+25b2- 2a2- 25b2+ a2- 10ba+25b2(a+5b)2(a-5b)2 = 2a2+ 50b2- 2a2+ 50b2(a2- 25b2)2 = 100b2(a2- 25b2)2;

4) x2+ 9x+18xy-3y-2x-6 – x+5y-2 = x2+ 9x+18yx+3- 2(x+3) – x+5y-2 = x2+ 9x+18x+3(y-2) – x+ 5\x+3y-2 = x2+ 9x+18-x+3(x+5)x+3(y-2) = x2+ 9x+18-(x2+ 5x+3x+15)x+3(y-2) = x2+ 9x+18- x2- 8x-15x+3(y-2) = x+3x+3(y-2) = 1y-2.