幫幫手!!

1.x²-y²+6y-9
=x²-(y²-6y+9)
=x²-(y-3) ²
=(x+y-3)(x-y+3)

2. (x-y)²+6(x-y)+9
=(x-y) ²+2(x-y)(3)+3²
=(x-y+3) ²

3.(x-y)²+6(x-y)+9-4z²
=(x-y) ²+2(x-y)(3)+3²-4z²
=(x-y+3) ²-(2z)²
=(x-y+3+2z)(x-y+3-2z)
=(x-y+2z+3)(x-y-2z+3)

1. x²-y²+6y-9
=x²-(y²-6y+9) Because a²-2ab+b² = (a+b)²
=x²-(y-3)²
=(x+y-3)(x-y+3) Because a²-b² = (a+b)(a-b)

2. (x-y)²+6(x-y)+9
=(x-y+3)²

3.(x-y)²+6(x-y)+9-4z²
=(x-y+3)²-(2z)² By part b
=(x-y+2z+3)(x-y-2z+3)

Notes, factorization mainly used the following identities:

1.a²-b² = (a+b)(a-b)
2. a²+2ab+b²=(a+b)²
3. a²-2ab+b² =(a-b)²