Вправи: 231

231. Спростіть вираз:

1) x4-y4 x2+y2-2xy : y+ x(x- y)2 = x4-y4 x2-2xy+y2 + (x- y)2y+ x • (x4-y4)•(x- y)2 (x2-2xy+y2)•(x+ y) = (x2- y2)(x2+y2)(x- y)2 (x- y)2•(x+ y) = (x- y)(x+ y)(x2+y2) x+ y = (x – y)(x² + y²);

2) a2+b2- ab x2- y2 : a3+b3 x2+y2-2xy = a2- ab+b2 x2- y2 • x2-2xy+y2 a3+ b3 = (a2- ab+b2)•(x2-2xy+y2) (x2- y2)(a3+ b3) = (a2- ab+b2)(x- y)2 x- yx+ ya+ b(a2- ab+b2) = x- y(x+ y)(a+ b).