Вправи: 416

416. Розклади на множники вираз.

а) x(a – 2) + y(a – 2) = (a – 2)(x + y);

б) (x + 1)² – 2x(x + 1) = (x + 1)(x + 1 – 2x) = (x + 1)(1 – x);

в) 2y(y – 6)³ – 3y(y – 6)² = y(y – 6)²(2y – 12 – 3) = y(y – 6)²(2y – 15);

г) 4(x – y) – 3a(y – x) = 4(x – y) + 3a(x – y) = (x – y)(4 + 3a);

ґ) 3(2x – 5) – 2x(5 – 2x) = 3(2x – 5) + 2x(2x – 5) = (2x – 5)(3 + 2x);

д) 6(m – n)² – m(n – m) = 6(n – m)² – m(n – m) = (n – m)(6n – 6m – m) = (n – m)(6n – 7m);

е) (4x – 3y)(x + 2y) + 2x(x + 2y) = (x + 2y)(4x – 3y + 2x) = (x + 2y)(6x – 3y);

є) (a + b)(x – y) + (b – a)(y – x) = (a + b)(x – y) – (b – a)(x – y) = (x – y)(a + b – b + a) = 2a(x – y).