Вправи: 331

331. Спростіть вираз.

а) xy2-x3 x2+ y2 • (x(x- y)2 – yx2-y2) + yx+ y = x2+y2 x2-y2;

1. x(x- y)2 – y(x- y)(x+ y) = xx+ y- y(x- y)(x- y)2(x+ y) = x2+ xy- yx+ y2(x- y)2(x+ y) = x2+y2 (x- y)2(x+ y);

2. x(y2-x2) x2+ y2 • x2+ y2(x- y)2(x+ y) = x(y- x)(y+ x)(x- y)2(x+ y) = xy- x;

3. xy- x + yx+ y = x2+ xy+y2- xy (y- x)(y+ x) = x2+y2 y2- x2.

б) 4a2+16+16aa-2 • (a2a-4 – a2+42a2-8 – 2a2+2a) = 4(a+2)a;

1. a2a-4 – a2+42a2-8 – 2a2+2a = a2(a-2) – a2-4 2(a2-4) – 2a(a+2) = a3+ 2a2- a3-4a-4a+82a(a-2)(a+2) = 2a2-8a+82a(a-2)(a+2) = 2(a2-4a+4)2a(a-2)(a+2) = 2(a-2)22a(a-2)(a+2) = a-2a(a+2);

2. 4a2+16+16aa-2 • a-2a(a+2) = 4(a+2)2a(a+2) = 4(a+2)a.