Розділ 2. РОЗКЛАДАННЯ МНОГОЧЛЕНІВ » 438

Подай вираз у вигляді добутку. a) xa + x + ya + y = (xa + x) + (ya + y) = x(a + 1) + y(a + 1) = (a + 1)(x + y); б) 3m – xm + 3n – xn = (3m – xm) + (3n – xn) = m(3 – x) + n(3 – x) = (3 – x)(m + n); в) 3c + 3y + ac + ay = (3c + 3y) + (ac + ay) = 3(c + y) + a(c + y) = (c + y)(3 + a); г) 2ax – 2at + 3x – 3y = (2ax – 2ay) + (3x – 3y) = 2a(x – y) + 3(x – y)(2a + 3). ґ) ax – ay – bx + by = (ax – ay) + (–bx + by) = a(x – y) – b(x – y) = (x – y)(a – b); д) ca + 2cx – na – 2nx = (ca + 2cx) – (na + 2nx) = c(a + 2x) – n(a + 2x) = (a + 2x)(c – n); е) 3m + 3n – am – an = (3m + 3n) – (am + an) = 3(m + n) – a(m + n)(3 – a); є) am – an – m + n = (am – an) – (m – n) = a(m – n) – (m – n) = (m – n)(a – 1); ж) a(x + y + z) + b(x + y + z) = (x + y + z)(a + b).