Решите 1) 12m^2-27n^2= 2) 4x^4-4x^3-4x^2+4x= 3)a^3+27b^3+a^2+6ab+9b^2=

1) 12m^2-27n^2=3(4m²-9n²)=3(2m-3n)(2m+3n)
2) 4x^4-4x^3-4x^2+4x=4x³(x-1)-4x(x-1)=(x-1)(4x³-4x)=4x(x-1)²(x+1)
3)a^3+27b^3+a^2+6ab+9b^2=(a+3b)(a²-3ab+9b²)+(a+3b)²=
=(a+3b)(a²-3ab+9b²+a+3b)

1) 12m² - 27n² = 3( 4m² - 9n²) = 3( 2m + 3n)(2m - 3n)
2) 4x⁴ - 4x³ - 4x² + 4x = ( 4x⁴ - 4x²) + ( 4x - 4x³) = 4x²( x² - 1) + 4x( 1 - x²)=
= 4x²( x² - 1) - 4x( x² - 1) = 4x(x² - 1)( x - 1) = 4x( x - 1)(x + 1)(x - 1) = 4x(x + 1)(x - 1)²
3) a³ + 27b³ + a² + 6ab + 9b² = ( a³ +(3b)³) + ( a² + 6ab +9b²) = (a + 3b)(a² - 3ab + 9b²)+
+ ( a + 3b)² = ( a + 3b)( a² - 3ab + 9b² + a + 3b)