Вправи: 1098

1098. Спрости вираз.

a) a+4a-3 – 4a2- 12a2- 3a+1 • a2+ 2a-3a2- 9 = a+4a-3 – 2a-1(2a+1)2a-1(a-1) • a+3(a-1)a-3(a+3) = a+4a-3 – 2a+1a-3 = a+4-2a-1a-3 = 3-aa-3 = –a-3a-3 = –1.

б) (2a-5a+2 – aa-3 + 15a2- a-6) : a-10a2+ 2a = (2a-5\a-3a+2 – a\a+2a-3 + 15a-3(a+2)) • a(a+2)a-10 = 2a2-6a-5a+15-a2-2a+15a+2(a-3) • a(a+2)a-10 = a2- 13a+30a-3 • aa-10 = a-10(a-3)a-3 • aa-10 = a.

в) (xx2+ 6x+8 – 2x2+ 3x+2 + 6x2+ 5x+4) • x2+ 2xx-3 – 3x-3 = (x\x+1x+4(x+2) – 2\x+4x+1(x+2) + 6\x+2x+4(x+1) • x(x+2)x-3 – 3x-3 = x2+ x-2x-8+6x+12x+1x+2(x+4) • x(x+2)x-3 – 3x-3 = x2+ 5x+4x+1(x+4) • xx-3 – 3x-3 = x+4(x+1)x+1(x+4) • xx-3 – 3x-3 = xx-3 – 3x-3 = x-3x-3 = 1.