Вправи: 1125

1125. Спростіть вираз:

1) (1x2+3x+2 + 2xx2+4x+3 + 1x2+5x+6)² • (x-3)2+12x2 = (1(x+1)(x+2) + 2x(x+1)(x+3) + 1(x+2)(x+3))² • x2-6x+9+12x2 = (x+3+2xx+2+x+1(x+1)(x+2)(x+3))² • x2+6x+92 = (2x2+6x+4(x+1)(x+2)(x+3))² • (x+3)22 = (2(x2+3x+2)(x+1)(x+2)(x+3))² • (x+3)22 = 4 • (x+3)2(x+3)2 • 2 = 2.

2) 3а2+2ab-b2a2+4ab+3b2 – 2 + 10(ab-3b2)a2-9b2 = (3a- b)(a+ b)(a+ b)(a+3b) – 2 + 10b(a-3b)(a-3b)(a+3b) = 3a- ba+3b – 2 + 10ba+3b = 3a- b-2a+3b+10ba+3b = 3a- b-2a-6b+10ba+3b = a+3ba+3b = 1.