Вправи: 439

439. Спростіть вираз:

1) 4m+18m2- 9 – 5m-3 + 1m+3 = 4m+18-5m+3+ (m-3)m-3(m+3) = 4m+18-5m-15+m-3m-3(m+3) = 0m2- 9 = 0;

2) 2x2x+3 + 53-2x – 4x2+ 94x2- 9 = 2x2x+3 – 52x-3 – 4x2+ 92x-3(2x+3) = 2x2x-3- 52x+3- 4x2- 92x-3(2x+3) = 4x2- 6x-10x-15-4x2- 92x-3(2x+3) = -16x-242x-3(2x+3) = -8(2x+3)2x-3(2x+3) = 83-2x;

3) 9x3xy+2y2 – 4y3x2+ 2xy = 9xy(3x+2y) – 4yx(3x+2y) = 9x2- 4y2xy(3x+2y) = 3x-2y(3x+2y)xy(3x+2y) = 3x-2yxy;

4) 4a4a2- 1 – 2a+16a-3 + 2a-14a+2 = 4a2a-1(2a+1) – 2a+13(2a-1) + 2a-12(2a+1) = 24a-2(2a+1)2+ 3(2a-1)262a-1(2a+1) = 24a-8a2- 8a-2+12a2- 12a+362a-1(2a+1) = 4a2+ 4a+162a-1(2a+1) = (2a+1)262a-1(2a+1) = 2a+16(2a-1);

5) 2x-1x2+ x+1 + 4x2+ 3x-7x3- 1 = 2x2- 2x-x+1+4x2+ 3x-7x-1(x2+ x+1) = 6x2- 6x-1(x2+ x+1) = 6x-1(x+1)x-1(x2+ x+1) = 6(x+1)x2+ x+1;

6) a23ab-2-a+6b – a3b-1.

Оскільки 3ab – 2 – a + 6b = 3b(a + 2) – (a + 2) = (3b – 1)(a + 2), то маємо a23b-1(a+2) – a3b-1 = a2- a2- 2a3b-1(a +2) = 2a1-3b(a+2).