Question

1. Упростите выражение: а) (3а+ 5) (За – 6) + 30; б) 8х - (3x+1)(5х + 1); в) (x-3)(x+5) - (х2+ х); г) (y+2)(y+3) - y(y - 1);​

Answer 1

Ответ:

1) (3a + 5)(3a - 6) + 30 = 3a * 3a + 3a * (- 6) + 5 * 3a + 5 * (- 6) + 30 = 9a2 - 18a + 15a - 30 + 30 = 9a2 - 3a;

2) 8х - (3х + 1)(5х + 1) = 8x - (3x * 5x + 3x * 1 + 1 * 5x + 1 * 1) = 8x - (15x2 + 3x + 5x + 1) = 8x - (15x2 + 8x + 1) = 8x - 15x2 - 8x - 1 = - 15x2 - 1;

3) (х - 3)(х + 5) - (х2 + х) = x2 + 5x - 3x - 15 - x2 - x = x - 15;

4) (у + 2)(у + 3) - у(у - 1) = y2 + 5y + 6 - y2 + y = 6y + 6;

Answer 2

а) (3a + 5) + (3a - 6) = 6a - 1

б) 8x - (3x + 1)(5x + 1) = 8x - (15x^2 + 3x + 5x + 1) = 8x - (15x^2 + 8x + 1) = -15x^2 + 1

в) (x - 3)(x + 5) - (x^2 + x) = x^2 + 5x - 3x - 15 - x^2 - x = x^2 - x - 15

г) (y + 2)(y + 3) - y(y - 1) = y^2 + 3y + 2y + 6 - (y^2 - y) = y^2 + 5y + 6 - y^2 + y = 6y + 6