Вправи: 159

159. Виконайте дії:

1) a3a+b + b3a+b = a3+ b3a+b = a+b(a2- ab+ b2)a+b = a² – ab + b²;

2) q3p-q – p3p-q = q3- p3p-q = q-p(q2- qp+ p2)p-q = -p-q(q2+ qp+ p2)p-q = –q² – qp – p²;

3) 2x3x+y – x3- y3x+y = 2x3- x3+ y3x+y = x3+ y3x+y = x+y(x2- xy+ y2)x+y = x² – xy + y².

4) 27x-3 – x3x-3 = 27-x3x-3 = 3-x(9+3x+x2)x-3 = -x-3(9+3x+ x2)x-3 = –9 – 3x – x²;

5) 8a-2 – a3a-2 = 8-a3a-2 = 2-a(4+2a+ a2)a-2 = -a-2(4+2a+ a2)a-2 = –4 – 2a – a².

6) aa3+ b3 + ba3+ b3 = a+ba3+ b3 = a+ba+b(a2- ab + b2) = 1a2- ab + b2;

7) bb3- c3 – bb3- c3 = c-bb3- c3 = -(b-c)b-c(b2+ bc + c2) = –1b2+ bc + c2;

8) 1x3+ 8 + 1+xx3+ 8 = 1+1+xx3+ 8 = 2+xx3+ 8 = 1x2- 2x+4;

9) a2+ b2a3+ b3 – aba3+ b3 = a2+ b2- aba+b(a2- ab + b2) = 1a+b;

10) c2b3- c3 + bc+b2b3- c3 = c2+ bc+ b2b3- c3 = c2+ bc+ b2b-c(b2+ bc + c2) = 1b-c.