№ 285 Алгебра = № 11.22 Математика
Умова:
Доведіть тотожність:
1) 10x – (–(5x + 20)) = 5(3x + 4);
2) –(–3p)–(–(8 – 5p)) = 2(4 – p);
3) 3(a – b – c) + 5(a – b) + 3c = 8(a – b).
Розв'язок:
1) 10x – (–(5x + 20)) = 10x – (–5x – 20)) = 10x + 5x + 20 = 15x + 20 = 5(3x + 4)
2) –(–3p)–(–(8 – 5p)) = 3p –(–8 + 5p) = 3p + 8 – 5p = 8 – 2p = 2(4 – p)
3) 3(a – b – c) + 5(a – b) + 3c = 3a – 3b – 3c + 5a – 5b + 3c = 3a – 3b – 3c + 5a – 5b + 3c = 8a – 8b = 8(a – b)