Вправи: 113

113. Спростіть вираз:

1) m+nm-n – m2+ n2m2- n2 = m+ n\m+nm-n – m2+ n2m-n(m+n) = (m+n)2- (m2+ n2)m-n(m+n) = m2+ 2mn+ n2- m2- n2 (m-n)(m+n) = 2mnm2- n2;

2) x-yx+y + y22xy+ x2+ y2 = x- y\x+yx+y + y2\1(x+y)2 = x+yx-y+ y2(x+y)2 = x2- y2+ y2(x+y)2 = x2(x+y)2;

3) 2a4a2- 1 – a+42a2+ a = 2a\a2a-1(2a+1) – a+ 4\2a-1a(2a+1) = 2a2- (2a-1)(a+4)a2a-1(2a+1) = 2a2- (2a2+ 8a-a-4)a2a-1(2a+1) = 2a2- 2a2- 7a+4a2a-1(2a+1) = 4-7a4a3- a;

4) b-2b2+ 6b+9 – bb2- 9 = b- 2\b-3(b+3)2 – b\b+3b-3(b+3) = b-2b-3- b(b+3)(b+3)2(b-3) = b2- 3b-2b+6- b2- 3b(b+3)2(b-3) = 6-8b(b+3)2(b-3);

5) x-6x2+ 3x + xx+3 – x-3x = x-6x2+ 3x + x\xx+3 – x- 3\x+3x = x-6+ x2- (x2- 9)x(x+3) = x-6+ x2- x2+ 9x(x+3) = x+3x(x+3) = 1x;

6) y+2y-2 – y-2y+2 – 16y2- 4 = y+ 2\y+2y-2 – y- 2\y-2y+2 – 16y2- 4 = (y+2)2- (y-2)2- 16y-2(y+2) = y2+ 4y+4-y2- 4y+4- 16y-2(y+2) = y2+ 4y+4- y2+ 4y-4-16y-2(y+2) = 8y-16y-2(y+2) = 8(y-2)y-2(y+2) = 8y+2.