Вправи: 103

103. Скоротіть дріб:

1) x3-2x3+ x x3- x2 = x(x2-2x+1)x2(x-1) = x(x-1)2x2(x-1) = x-1x;

2) y4-4y2 y3+ 4y2+4y = y2(y2-4)y(y2+4y+4) = y2(y-2)(y+2)y(y+2)2 = y(y-2)y+2;

3) a3-16ab2 a2b+8ab2+ 16b3 = a(a2-16b2) b(a2+8ab+16b2) = a(a-4b)(a+4b)b(a+4b)2 = a(a-4b)b(a+4b);

4) c4-6c3+9c2 9c- c3 = c2(c2-6c+9)c(9- c2) = c2(c-3)2c(3- c)(3+ c) = c(3- c)23- c(3+ c) = c(3- c)3+ c.