Вправи: 109

109. Спростіть вираз:

1) 4x- yx2-y2 + 1x- y = 4x- y(x- y)(x+ y) + 1\x+yx- y = 4x- y+ x+ y(x- y)(x+ y) = 5xx2-y2;

2) y2y3-81 – yy+9 = y2(y-9)(y+9) – y\y-9y+9 = y2-y(y-9)(y-9)(y+9) = y2-y2+9y(y-9)(y+9) = 9yy2-81;

3) 10a25a2-9 – 15a+3 = 10a(5a-3)(5a+3) – 1\5a-35a+3 = 10a-(5a-3)(5a-3)(5a+3) = 10a-5a+3(5a-3)(5a+3) = 5a+3(5a-3)(5a+3) = 15a-3;

4) nn-7 – n2n2-14n+49 = n\n-7n-7 – n2(n-7)2 = nn-7-n2 (n-7)2 = n2-7n-n2 (n-7)2 = –7n(n-7)2.