Вправи: 825

825. Виконайте дії:

1) 2a- 1\2a-4 – 3a+22(a-4) = 22a-1- (3a+2)2(a-4) = 4a-2-3a-22(a-4) = a-42(a-4) = 12;

2) x+23x+9 – 4-x5x+15 = x+ 2\53(x+3) – 4- x\35(x+3) = 5x+2- 3(4-x)5(x+3) = 5x+10-12+3x15(x+3) = 8x-215x+45;

3) m+ 1\m+3m-3 – m+ 2\m-3m+3 = m+1m+3- (m+2)(m-3)m-3(m+3) = m2+ m+3m+3-(m2+ 2m-3m-6)m-3(m+3) = m2+ 4m+3- m2+ m+6m-3(m+3) = 5m+9m-3(m+3);

4) xx+y – 2y2y2- x2 – yx-y = x\x-yx+y – 2y2x-y(x+y) – y\x+yx-y = xx-y+ 2y2- y(x+y)x-y(x+y) = x2- xy+2y2- xy- y2x-y(x+y) = x2- 2xy+ y2x-y(x+y) = (x-y)2x-y(x+y) = x-yx+y;

5) m3m-2n – 3m2- 3mn9m2- 12mn+4n2 = m\3m-2n3m-2n – 3m2- 3mn(3m-2n)2 = m3m-2n- (3m2- 3mn)(3m-2n)2 = 3m2- 2mn-3m2+ 3mn(3m-2n)2 = mn(3m-2n)2;

6) a+3a2- 2a – a-25a-10 + a+25a = a+ 3\5a(a-2) – a- 2\a5(a-2) + a+ 2\a-25a = 5a+3- aa-2+ (a-2)(a+2)5a(a-2) = 5a+15- a2+ 2a+ a2- 45a(a-2) = 7a+115a2- 10a;

7) 33(a-3) – a-12a2- 4a+2 = 33(a-3) – a-12(a-1)2 = 1\2a-3 – 12(a-1) = 2-12(a-1) = 12a-2;

8) 2 – 14m-2 – m = 2- m\m-21 – 14m-2 = -(m-2)2- 14m-2 = -m2- 4m+4- 14m-2 = -m2+ 4m-4-14m-2 = -m2+ 4m-18m-2;

9) 2x+1x2- 6x+9 – 8x2- 9 – 2x-1x2+ 6x+9 = 2x+ 1\(x+3)2(x-3)2 – 8\x-3(x+3)x-3(x+3) – 2x- 1\(x-3)2(x+3)2 =2x+1x2+ 6x+9- 8x2- 9- (2x-1)(x2- 6x+9)(x-3)2(x+3)2 = 2x3+ 12x2+ 18x+ x2+ 6x+9-8x2+ 72-(2x3- 12x2+ 18x- x2+ 6x-9)(x-3)2(x+3)2 = 2x3+ 13x2+ 24x+9-8x2+ 72-2x3+ 13x2- 24x+9(x-3)2(x+3)2 = 148x2+ 90(x-3)2(x+3)2.