Вправи: 164 (1-3)

164. Спростіть вираз:

1) yyx-x2 – yyx+x2 = y\y+xx(y-x) – y\y-xx(y+x) = y2+ xy- y2+ xyxy-x(y+x) = 2xyx(y2- x2) = 2yy2- x2;

2) 4xx2- y2 – x+yxy-y2 = 4x\yx-y(x+y) – x+y\x+yy(x-y) = 4xy-(x+y)2yx-y(x+y) = 4xy-(x2+ 2xy+ y2)yx-y(x+y) = 4xy-x2- 2xy-y2yx-y(x+y) = -x2+ 2xy- y2yx-y(x+y) = -(x-y)2yx-y(x+y) = –x-yy(x+y) = y-xy(x+y);

3) a-3\a(a-3)a+3 – a+3\a(a+3)a-3 + 12\a+3(a-3)a = a(a-3)2- a(a+3)2+ 12(a2- 9)aa-3(a+3) = a(a2- 6a+9)-a(a2+ 6a+9)+ 12a2- 108a(a2- 9) = a3- 6a2+ 9a- a3- 6a2- 9a+ 12a2- 108a(a2- 9) = – 108a(a2- 9) = 108a(9-a2);

4) 1-tt2- t – t+11-t2 = 1-tt(t-1) – t+11-t(1+t) = –t-1t(t-1) + t+1t-1(t+1) = –1\t-1t + 1\tt-1 = -t+1+tt(t-1) = 1t(t-1);

5) a2(a-3)2 + a3-a = a2(3-a)2 + a\3-a3-a = a2+ 3a- a2(3-a)2 = 3a(3-a)2;

6) b+1(b-1)2 + 21-b2 – 1b+1 = b+1\1+b(1-b)2 + 2\1-b1-b(1+b) – 1\(1-b)21+b = (1+b)2+ 2-2b-(1-2b+ b2)1-b2(1+b) = 2b+21-b2(1+b) = 2(b+1)1-b2(1+b) = 2(1-b)2.