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ГДЗ Алгебра 7 клас Мерзляк (2024)
§ 1. Алгебраїчні вирази
Реклама:
Розкладіть на множники:
1) (m – 9)2 – 3(m – 9) = (m – 9)(m – 9 – 3) = (m – 9)(m – 12);
2) a(a + 5)2 + (a + 5) = (a + 5)(a(a + 5) + 1) = (a + 5 )(a2 + 5a + 1);
3) (m2 – 3) – n(m2 – 3)2 = (m2 – 3)(1 – n(m2 – 3)) = (m2 – 3)(1 – nm2 + 3n);
4) 8c(p – 12) + 7d(p – 12)2 = (p – 12)(8c + 7d(p – 12)) = (p – 12) (8c + 7dp – 84d).
5) a(2a + b)(a + b) – 4a(a + b)2 = a(a + b)(2a + b – 4(a + b)) = a(a + b)(2a + b – 4a – 4b) = a(a + b)(–2a – 3b) = –a(a + b)(2a + 36);
6) 3m2(m – 8) + 6m(m – 8)2 = 3m(m – 8)(m + 2(m – 8)) = 3m(m –8) ∙ (m + 2m – 16) = 3m(m – 8)(3m – 16);
7) (2a + 3)(a + 5) + (a – 1)(a + 5) = (a + 5)(2a + 3 + a – 1) = (a + 5)(3a + 2);
8) (3x + 7)(4y – 1) – (4у – 1)(2x + 10) = (4у – 1)(3x + 7 – (2x + 10)) = (4y – 1)(3x + 7 – 2x – 10) = (4y – 1)(x – 3);
9) (5m – n)3(m + 8n)2 – (5m – n)2(m + 8n)3 = (5m – n)2(m + 8n)2(5m – n – (m + 8n)) = (5m – n)2(m + 8n)2(5m – n – m – 8n) = (5m – n)2 ∙ (m + 8n)2(4m – 9n).
1) (m – 9)2 – 3(m – 9) = (m – 9)(m – 9 – 3) = (m – 9)(m – 12);
2) a(a + 5)2 + (a + 5) = (a + 5)(a(a + 5) + 1) = (a + 5 )(a2 + 5a + 1);
3) (m2 – 3) – n(m2 – 3)2 = (m2 – 3)(1 – n(m2 – 3)) = (m2 – 3)(1 – nm2 + 3n);
4) 8c(p – 12) + 7d(p – 12)2 = (p – 12)(8c + 7d(p – 12)) = (p – 12) (8c + 7dp – 84d).
5) a(2a + b)(a + b) – 4a(a + b)2 = a(a + b)(2a + b – 4(a + b)) = a(a + b)(2a + b – 4a – 4b) = a(a + b)(–2a – 3b) = –a(a + b)(2a + 36);
6) 3m2(m – 8) + 6m(m – 8)2 = 3m(m – 8)(m + 2(m – 8)) = 3m(m –8) ∙ (m + 2m – 16) = 3m(m – 8)(3m – 16);
7) (2a + 3)(a + 5) + (a – 1)(a + 5) = (a + 5)(2a + 3 + a – 1) = (a + 5)(3a + 2);
8) (3x + 7)(4y – 1) – (4у – 1)(2x + 10) = (4у – 1)(3x + 7 – (2x + 10)) = (4y – 1)(3x + 7 – 2x – 10) = (4y – 1)(x – 3);
9) (5m – n)3(m + 8n)2 – (5m – n)2(m + 8n)3 = (5m – n)2(m + 8n)2(5m – n – (m + 8n)) = (5m – n)2(m + 8n)2(5m – n – m – 8n) = (5m – n)2 ∙ (m + 8n)2(4m – 9n).