В решении.
Объяснение:
1) 5а³ - 125аb² = 5a(a² - 25b²) = 5a(a - 5)(a + 5);
2) a² - b² - 5a + 5b =
= (a² - b²) - (5a - 5b) =
= (a - b)(a + b) - 5(a - b) =
= (a - b)(a + b - 5);
3) а²- 2ав + в² - ас + вс =
= (а²- 2ав + в²) - (ас - вс) =
= (a - b)² - c(a - b) =
= (a - b)(a - b - c);
4) 25a² + 70ab + 49b² =
= (5a + 7b)² =
= (5a + 7b)(5a + 7b);
5) a² - 2ab + b² - 3a + 3b =
= (a² - 2ab + b²) - (3a - 3b) =
= (a - b)² - 3(a - b) =
= (a - b)(a - b - 3);
6) 63ab³ - 7a²b =
= 7ab(9b² - a);
7) (b - c)(b + c) - b(b + c) =
= (b + c)(b - c - b) =
= -c(b + c);
8) m² + 6mn + 9n² - m - 3n =
= (m² + 6mn + 9n²) - (m + 3n) =
= (m + 3n)² - (m + 3n) =
= (m + 3n)(m + 3n - 1);
9) a² - 9b² + a - 3b =
= (a² - 9b²) + (a - 3b) =
= (a - 3b)(a + 3b) + (a - 3b) =
= (a - 3b)(a + 3b + 1).
log a (a^2/b) log a (a^2) - log a (b)
5log (b^2)/a (a^2/b)= 5· = 5· =
log a (b^2)/a log a (b^2)-log a (a)
2- 3 (-1)
= 5 = 5 = -1
2·3 -1 5
2) log 2 (a^1/3) , если log 4 (a^3)=9
log 4 (a^3)=9 ⇔3 log 4 (a)=9 ⇔ log 4 (a)=3
log 4 (a^1/3) (1/3)log 4 (a) 1log 2 (a^1/3) = = = = 2
log 4 (2) log 4 (√4) 1/2
3) lg2.5 если log 4(125) = a
log 4(125) = a ⇔ log 4(5³) =3 log 4(5) =a ⇔ log 4(5)=a/3
log 4 (5/2) log 4 (5)-log 4 (2) a/3-1/2 2a-3lg2.5 = = = =
log 4 (5·2) log 4 (5) +log 4 (2) a/3 +1/2 2a+3
В решении.
Объяснение:
1) 5а³ - 125аb² = 5a(a² - 25b²) = 5a(a - 5)(a + 5);
2) a² - b² - 5a + 5b =
= (a² - b²) - (5a - 5b) =
= (a - b)(a + b) - 5(a - b) =
= (a - b)(a + b - 5);
3) а²- 2ав + в² - ас + вс =
= (а²- 2ав + в²) - (ас - вс) =
= (a - b)² - c(a - b) =
= (a - b)(a - b - c);
4) 25a² + 70ab + 49b² =
= (5a + 7b)² =
= (5a + 7b)(5a + 7b);
5) a² - 2ab + b² - 3a + 3b =
= (a² - 2ab + b²) - (3a - 3b) =
= (a - b)² - 3(a - b) =
= (a - b)(a - b - 3);
6) 63ab³ - 7a²b =
= 7ab(9b² - a);
7) (b - c)(b + c) - b(b + c) =
= (b + c)(b - c - b) =
= -c(b + c);
8) m² + 6mn + 9n² - m - 3n =
= (m² + 6mn + 9n²) - (m + 3n) =
= (m + 3n)² - (m + 3n) =
= (m + 3n)(m + 3n - 1);
9) a² - 9b² + a - 3b =
= (a² - 9b²) + (a - 3b) =
= (a - 3b)(a + 3b) + (a - 3b) =
= (a - 3b)(a + 3b + 1).