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ГДЗ Алгебра 7 клас Тарасенкова (2024)
Роздiл 3. Одночлени i многочлени
Реклама:
Доведіть тотожність:
1) (a + b)2 – (–a – b)2 = 0; (a + b + (–a – b))(a + b – (–a – b)) = (a + b – a – b)(a + b + a + b) = 0 • (2a + 2b) = 0;
2) (a + b)2 – (a – b)2 = (a + b + a – b)(a + b – a + b) = 2a • 2b = 4ab;
3) (b – а)2 – (b – а)(b + а) = (b – а)2 – (b2 – а2) = b2 – 2аb + a2 – b2 + а2 = 2a2 – 2ab = 2a(a – b).
1) (a + b)2 – (–a – b)2 = 0; (a + b + (–a – b))(a + b – (–a – b)) = (a + b – a – b)(a + b + a + b) = 0 • (2a + 2b) = 0;
2) (a + b)2 – (a – b)2 = (a + b + a – b)(a + b – a + b) = 2a • 2b = 4ab;
3) (b – а)2 – (b – а)(b + а) = (b – а)2 – (b2 – а2) = b2 – 2аb + a2 – b2 + а2 = 2a2 – 2ab = 2a(a – b).