Question

Разложите на множители:
1) а^2-b^2+2(a+b)^2
2)b^2-c^2-10(b-c)^2
3)2(x-y)^2+3x^2-3y^2
4)5a^2-5-4(a+1)^2

Answer 1

1) а²-b²+2(a+b)² =  (а-b)(а+b)+2(a+b)² = (a+b)·(a-b+2a+2b)=

 = (a+b)·(3a+b)

2) b²-c²-10(b-c)² = (b-c)(b+c)  - 10(b-c)²= (b-c)·(b+c-10b+10c)=

 =  (b-c)·(11c-9b)

3) 2(x-y)² + 3x²-3y² = 2(x-y)² + 3(x²-y²) =  2(x-y)² + 3(x-y)·(x+y) =

   = (x-y)·(2x-2y+3x+3y) = (x-y)·(5x+y)

       

4) 5a²-5-4(a+1)² = 5(a²-1) - 4(a+1)² = 5(a-1)·(a+1) - 4(a+1)² =

  = (a+1)·(5a-5 - 4a-4) =  (a+1)·(a-9)