Вправи: 230

230. Спростіть вираз:

1) x3+y3 x- y : x+ yx3-y3 = x3+y3 x- y • x3-y3 x+ y = (x3+y3)• (x3-y3) (x- y)(x+ y) = x6- y6x2- y2 = (x2)3-(y2)3 x2-y2 = (x2-y2)(x4+x2y2+y4) x2- y2 = x⁴ + x²y² + y⁴;

2) a2+ aba2+b2 : a2+2ab+b2 a4-b4 = a2+ aba2+b2 • a4-b4 a2+2ab+b2 = (a2+ ab)(a4-b4) (a2+ b2)(a2+2ab+ b2) = aa+ b(a2-b2)( a2+b2) (a2+ b2)(a+ b)2 = a(a- b)(a+ b)a+ b = a(a – b).