Question

SOS!15 БАЛЛОВ!
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Answer 1

1) 3m - 3n + (m - n)² = 3(m - n) + (m - n)² = (m - n)(3 + m - n)

2) x + y + x² - y² = (x + y) + (x² - y)² = (x + y) + (x + y)(x - y) = (x + y)(1 + x - y)

3) 9m² + 6mn + n² - 25 = (9m² + 6mn + n²) - 25 = (3m + n)² - 5² =

= (3m + n - 5)(3m + n + 5)

4) ac⁵ - c⁵ - ac³ + c³ = (ac⁵ - c⁵) - (ac³ - c³) = c⁵(a - 1) - c³(a - 1) = (a - 1)(c⁵ - c³)=

c³(c² - 1)(a - 1) = c³(c - 1)(c + 1)(a - 1)

Answer 2

$1)\; \; 3m-3n+(m-n)^2=3(m-n)+(m-n)^2=(m-n)(3+m-n)\\\\2)\; \; x+y+x^2-y^2=(x+y)+(x-y)(x+y)=(x+y)(1+x-y)\\\\3)\; \; 9m^2+6mn+n^2-25=(3m+n)^2-5^2=\\\\=(3m+n-5)(3m+n+5)\\\\4)\; \; ac^5-c^5-ac^3+c^3=c^5(a-1)-c^3(a-1)=\\\\=(a-1)(c^5-c^3)=(a-1)\cdot c^3(c^2-1)=\\\\=c^3\cdot (a-1)(c-1)(c+1)$