Вправи: 106

106. Скоротіть дріб:

1) a2-b2- c2-2bc a2+ b2- c2-2ab = a2- (b+ c)2(a+ b)2- c2 = (a-b+ c)(a+ b+ c)(a+ b- c)(a+ b+ c) = a-b - ca+ b- c;

2) a- b(c- d)(b2- a2)(d2-c2) = (a- b)(c- d)(b- a)(b+ a)(d- c)(d+ c) = a- b(c- d)(a- b)(a+ b)(c- d)(c+ d) = 1(a+ b)(c+ d);

3) x2+ xy+ yz-z2 y2- x2+2xz-z2 = x2-z2+ y(x+ z) y2- (x- z)2 = x- zx+ z+ y(x+ z)(y-x- z)(y+(x- z) = x+ z(x- z+ y)(y- x+ z)(x- z + y) = x+ zy- x+ z;

4) 25- a2-2ab- b2 a2+ ab+5b-25 = 25-(a+ b)2(a2-25)+(ab+5b) = (5-a+ b)(5+(a+ b)a-5a+5+ b(a+5) = (5- a- b)(5+ a+ b)(a+5)(a-5+ b) = –(a+ b-5)(a+ b+5)(a+5)(a+ b-5) = –a+ b+5a+5.