разложите на множители пожалуйста
1)ax-bx-x+ay-by-y=
2)2a^(2)-a+2ab-b-2ac+c=
3)a^(5)-a^(4)b+a^(3)b^(2)-a^(2)b^(3)+ab^(4)-b^(5)
4)px^(2)+gx+g^(2)y+pgxy+p^(2)gx+pg^(2)
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разложите на множители пожалуйста
1)ax-bx-x+ay-by-y=
2)2a^(2)-a+2ab-b-2ac+c=
3)a^(5)-a^(4)b+a^(3)b^(2)-a^(2)b^(3)+ab^(4)-b^(5)
4)px^(2)+gx+g^(2)y+pgxy+p^(2)gx+pg^(2)
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Answers & Comments
1) ax - bx - x + ay - by - y = (ax + ay) - (bx + by) - (x + y) =
a(x + y) - b(x + y) - (x + y) = (a - b - 1)(x + y)
2) 2a^(2) - a + 2ab - b - 2ac + c = (2a^(2)) - (b + c) - (2ab + 2ac) =
a(2a - 1) - (b + c) - 2a(b + c) = a(2a - 1) - (1 - 2a)(b + c) =
a(2a - 1) + (2a - 1)(b + c) = (a + b + c)(2a - 1)
3) a^(5) - a^(4)b + a^(3)b^(2) - a^(2)b^(3) +ab^(4) - b^(5) =
(a^(5) - a^(4)b + a^(3)b^(2)) - (a^(2)b^(3) - ab^(4) - b^(5)) =
a^(3)(a^(2) - ab +b^(2)) - b^(3)(a^(2) - ab + b^(2)) = (a^(3)-b^(3))(a^(2) - ab + b^(2))