Вправи: 161 (1-4)

161. Спростіть вираз:

1) a2+ b2(a+b)2 + 2ab(a+b)2 = a2+ b2+ 2ab(a+b)2 = (a+b)2(a+b)2 = 1;

2) q3(p-q)2 – p3(p-q)2 = q3- p3(p-q)2 = q-p(q2+ qp+ p2)(p-q)2 = q2+ qp+ p2(p-q)2.

3) 2x2(x+y)2 – 2y2(x+y)2 = 2x2- 2y2(x+y)2 = 2(x2- y2)(x+y)2 = 2x+y(x+y)(x+y)2 = 2(x-y)x+y.

4) 4x2(2x-y)2 – y2(y-2x)2 = 4x2(2x-y)2 – y2(2x-y)2 = 4x2- y2(2x-y)2;

5) 125(x-5)2 – x3(x-5)2 = 125-x3(x-5)2 = 53- x3(x-5)2 = 5-x(25+5x+x2)(x-5)2 = 25+5x+x25-x = x2+ 5x+255-x;

6) 3(x+2)3 + x2+ 4x+1(x+2)3 = 3+x2+ 4x+1(x+2)3 = x2+ 4x+4(x+2)3 = (x+2)2(x+2)3 = 1x+2;

7) 32-14x(x-3)2 – 26-12x(3-x)2 = 32-14x(x-3)2 – 26-12x(x-3)2 = 32-14x-26+12x(x-3)2 = -2x+6(x-3)2 = -2(x-3)(x-3)2 = –2x-3;

8) x2+ 8yx-4(y+3) + 4(x+2y)4-x(3+y) = x2+ 8yx-4(y+3) – 4(x+2y)x-4(y+3) = x2+ 8y-4x-8yx-4(y+3) = x2-4xx-4(y+3) = x(x-4)x-4(y+3) = xy+3.