(y²+3y)²—(2y+6)²分解因式
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/20 22:31:38
![(y²+3y)²—(2y+6)²分解因式](/uploads/image/z/7631621-53-1.jpg?t=%28y%26%23178%3B%2B3y%29%26%23178%3B%E2%80%94%282y%2B6%29%26%23178%3B%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F)
(y²+3y)²—(2y+6)²分解因式
(y²+3y)²—(2y+6)²分解因式
(y²+3y)²—(2y+6)²分解因式
答:平方差、十字相乘法:
(y²+3y)²—(2y+6)²
=(y²+3y-2y-6)(y²+3y+2y+6)
=(y²+y-6)(y²+5y+6)
=(y-2)(y+3)(y+2)(y+3)
=(y-2)(y+2)(y+3)²
(y²+3y)²—(2y+6)²
=(y²+3y+2Y+6)(y²+3y-2Y-6)
=(Y²+5y+6)(y²+y-6)
=(y-2)(y+3)(y+2)(y+3)
=(y-2)(y+2)(y+3)²
(y^2+3y)^2-(2y+6)^2=y^2(y+3)^2-4(y+3)^2=(y-2)(y+2)(y+3)^2
原式=(y²+3y+2y+6)*(y²+3y-2y-6)
=(y²+5y+6)*(y²+y-6)
=(y²+5y+6)(x+3)(x-2)