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ГДЗ Алгебра 7 клас Істер (2024)
2. ЦІЛІ ВИРАЗИ
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855. Розкладіть на множники:
1) a4 – 81 = (a2)2 – 92 = (a2 – 9)(a2 + 9) = (a – 3)(a + 3)(a2 + 9);
2) 16 – c4 = 42 – (c2) = (4 – c2)(4 + c2) = (2 – c)(2 + c)(4 + c2);
3) x8 – 1 = (x4)2 – 1 = (x4 – 1)(x4 + 1) = (x2 – 1)(x2 + 1)(x4 + 1) = (x – 1)(x + 1) ∙ (x2 + 1)(x4 + 1);
4) a4 – b8 = (a2)2 – (b4)2 =(a2 – b4)(a2 + b4) =(a – b2)(a + b2)(a2 + b4).
856. Доведіть тотожність:
a8 – b8 = (a4)2 – (b4)2 = (a4 – b4)(a4 + b4) = (a2 – b2)(a2 + b2) (a4 + b4) = (a – b)(a + b)(a2 + b2)(a4 + b4) — тотожність доведена.
1) a4 – 81 = (a2)2 – 92 = (a2 – 9)(a2 + 9) = (a – 3)(a + 3)(a2 + 9);
2) 16 – c4 = 42 – (c2) = (4 – c2)(4 + c2) = (2 – c)(2 + c)(4 + c2);
3) x8 – 1 = (x4)2 – 1 = (x4 – 1)(x4 + 1) = (x2 – 1)(x2 + 1)(x4 + 1) = (x – 1)(x + 1) ∙ (x2 + 1)(x4 + 1);
4) a4 – b8 = (a2)2 – (b4)2 =(a2 – b4)(a2 + b4) =(a – b2)(a + b2)(a2 + b4).
856. Доведіть тотожність:
a8 – b8 = (a4)2 – (b4)2 = (a4 – b4)(a4 + b4) = (a2 – b2)(a2 + b2) (a4 + b4) = (a – b)(a + b)(a2 + b2)(a4 + b4) — тотожність доведена.