1.
в) 1-5d² - d-5 + 1 = 1-5d² -d²(d-5)+d³ = 1-5d²-d³+5d²+d³ = 1
d⁶ d⁴ d³ d⁶ d⁶ d⁶
г) 5c - 4c + c² = 5c - 4c + c² =
6c-6 3c+3 2c²-2 6(c-1) 3(c+1) 2(c²-1)
= 5c - 4c + c² = 5c(c+1) -2*4c(c-1) + 3c² =
6(c-1) 3(c+1) 2(c-1)(c+1) 6(c-1)(c+1)
=5c²+5c -8c²+8c+3c² = 13c
6(c-1)(c+1) 6c²-6
2.
a) 3c+2 - 5 = 3c+2 - 5 = 3c+2 -5(c-2) =
c²-4c+4 c-2 (c-2)² c-2 (c-2)²
=3c+2-5c+10 = 12-2c
(c-2)² (c-2)²
б) 2mn + 2m - 1 = 2mn + 2m - 1 =
m³+n³ m²-n² m-n (m+n)(m²-mn+n²) (m-n)(m+n) m-n
=2mn(m-n)+2m(m²-mn+n²)-m³-n³ = 2m²n-2mn²+2m³-2m²n+2mn²-m³-n³ =
(m+n)(m-n)(m²-mn+n²) (m+n)(m-n)(m²-mn+n²)
= m³ - n³ = (m-n)(m²+mn+n²) = m²+mn+n²
(m+n)(m-n)(m²-mn+n²) (m+n)(m-n)(m²-mn+n²) m³+n³