Вправи: 417

417. Розклади на множники вираз.

a) a(a² + 1) + 5(a² + 1) = (a² + 1)(a + 5);

б) 8(a² – 3) + (a² – 3)² = (a² – 3)(8 + a² – 3) = (a² – 3)(a² + 5)

в) 5b(3 + 2c)³ + 2b(3 + 2c)² = b(3 + 2c)²(15 + 10c + 2) = b(3 + 2c)²(10c + 17);

г) x(a – b) + 3y(b – a) = x(a – b) – 3y(a – b) = (a – b) • (x – 3y);

ґ) 4(b – 3) + 5b(3 – b) = 4(b – 3) – 5b(b – 3) = (b – 3)(4 – 5b);

д) 7(a – 4)² + (4 – a) = 7(4 – a)² + (4 – a) = (4 – a)(28 – 7a + 1) = (4 – a)(29 – 7a);

е) 5a(3a – b) + (b – 3a)(5a + 2b) = 5a(3a – b) – (3a – b)(5a + 2b) = –2b(3a – b);

є) (a + 7b)(a – 5b) – (b – 3a)(a – 5b) = (a – 5b)(a + 7b – b + 3a) = (a – 5b)(4a + 6b).