Вопрос от посетителя
I.Разложите на множетели многочлены:^-значит степень
а).a^2+ad-a-d
b).y^3-xy^2+y-x
B).3ab-b^2+3a^2-ab
г).6y^2-3y+2ay-a
II.Разложите на множители:
a).ax-a+bx-b+cx-c
b).ax+bx-ay-by+az+bz
B).ax-bx-x+ay-by-y
III.Сократите дроби:^-значит степень
ax-ay-bx-by
а).————–
x^2+xy
ax-ay-x^2+xy
B).—————-
ax-a^2
Отвечает Илюха:
1. a) a^2 + ad – a – d = (a^2 – a) + (ad – d) = a(a – 1) + d(a -1) = (a – 1)(a+d)
b) y^3 – xy^2 + y – x = (y^3 + y) – (xy^2 + x) = y(y^2 + 1) – x(y^2 + 1) = (y^2 + 1)(y – x)
c) 3ab – b^2 + 3a^2 – ab = (3ab + 3a^2) – (b^2 + ab) = 3a(b + a) – b(b+a) = (3a – b)(b + a)
d) 6y^2 – 3y + 2ay – a = (6y^2 – 3y) + (2ay – a) = 3y(2y – 1) + a(2y – 1) = (3y + a)(2y – 1)
2. a) ax – a + bx -b + cx – c = a(x – 1) + b(x – 1) + c(x -1) = (a+b+c)(x – 1)
b) ax + bx – ay – by + az + bz = x(a+b) – y(a+b) + z(a + b) = (a + b)(x + z – y)
c) ax – bx – x + ay – by – y = x(a – b – 1) + y(a – b – 1) = (x + y)(a – b – 1)
3. b) (ax – ay – x^2 + xy) / (ax – a^2) = ( (a-x – a)(y – x)) / (a(x – a)) = (y – x) / a