因式分解：（1）49（x+y）²-9（x-y）² （2）（x²-5）²+8（x²-5）+16

因式分解：（1）49（x+y）²-9（x-y）² （2）（x²-5）²+8（x²-5）+16
因式分解：（1）49（x+y）²-9（x-y）² （2）（x²-5）²+8（x²-5）+16

因式分解：（1）49（x+y）²-9（x-y）² （2）（x²-5）²+8（x²-5）+16
49（x+y）²-9（x-y）²
=(7x+7y+3x-3y)(7x+7y-3x+3y)
=(10x+4y)(4x+10y)
=4(5x+2y)(2x+5y)
（x²-5）²+8（x²-5）+16
=(x²-5+4)²
=(x²-1)²
=(x-1)²(x+1)²

（1）49（x+y）²-9（x-y）² =[7(x+y)+3(x-y)][7(x+y)-3(x-y)]=[10x+4y][4x+10y]=4(5x+2y)(2x-5y)
（2）（x²-5）²+8（x²-5）+16=[(x²-5)+4]²=[x²-1]²

40(X+Y)²+9(X+Y)²-9（x-y）²=4(5X+2Y)(2X+5Y)
（x²-5）²+8（x²-5）+16 =(x²-5+4)²=(x²-1)²

(1)=[7(x+y)+3(x-y)][7(x+y)-3(x-y)]
=[7x+7y+3x-3y][7x+7y-3x+3y]
=(10x+4y)(4x+10y)
(2)=(x²-5+4)
=(x²-1)
=(x+1)(x-1)