Разложите многочлен на множители: 1)ax+ay+bx+by 2)ax-ay+bx-by 3)a^2 +ab+ac+bc 4)ax+ay+6x+6y 5)1-bx-x+b 6)ab+2b-2a-4 7)x^2

Раскладывать на множители будем способом группировки.1) аx + ay + bx + by = (аx + ay) + (bx + by) = a(x + y) + b(x + y) = (x + y)(a + b);2) ax – ay + bx – by = (ax – ay) + (bx – by) = a(x – y) + b(x – y) = (x – y)(a + b);3) a^2 + ab + ac + bc = (a^2 + ab) + (ac + bc) = a(a + b) + c(a + b) = (a + b)(a + c);4) ax + ay + 6x + 6y = (ax + ay) + (6x + 6y) = a(x + y) + 6(x + y) = (x + y)(a + 6);5) 1 – bx – x + b = (1 – x) + (b – bx) = 1(1 – x) + b(1 – x) = (1 – x)(1 + b);6) ab + 2b - 2a – 4 = (ab + 2b) + (- 2a – 4) = b(a + 2) – 2(a + 2) = (a + 2)(b – 2);7) x^2 + xy + ax + ay = (x^2 + xy) + (ax + ay) = x(x + y) + a(x + y) = (x + y)(x + a);8) am – an + m – n = (am + m) + (- an – n) = m(a + 1) – n(a + 1) = (a + 1)(m – n);9) 3x - 3y + ax – ay = (3x - 3y) + (ax – ay) = 3(x – y) + a(x – y) = (x – y)(3 + a);10) ab - a^2 + 2a - 2b = (ab - a^2) + (2a - 2b) = a(b – a) – 2(b – a) = (b – a)(a – 2).