Розділ 2. РОЗКЛАДАННЯ МНОГОЧЛЕНІВ » 629

Розклади на множники многочлен. a) x – a + x2 – a2 = (x – a) + (x2 – a2) = (x – a) + (x – a)(x + a) = (x – a)(1 + x + a); б) a2 – b2 + a – b = (a2 – b2) + (a – b) = (a – b)(a + b) + (a – b) = (a – b)(a + b + 1); в) 2k + 3p + 4k2 – 9p2 = 2k + 3p + (4k2 – 9p2) = 2k + 3p + (2k + 3p)(2k – 3p) = (2k + 3p)(1 + 2k – 3p); г) c2 – c – m2 – m = c2 – m2 – (c + m) = (c – m)(c + m) – (c + m) = (c + m)(c – m – 1); ґ) a3 + b3 – a – b = (a3 + b3) – (a + b) = (a + b)(a2 – ab + b2) – (a + b) = (a + b) = (a + b)(a2 – ab + b2 – 1); д) x – y – x3 + y3 = (x – y) – (x3 – y3) = (x – y) – (x – y)(x2 + xy + y2) = (x – y)(1 – (x2 + xy + y2)) = (x – y)(1 – x2 – xy – y2).