用十字乘法因式分解,好的追加分:8x^2y^2+6xy-35 2(a+b)^2+(a+b)(a-b)-6(a-b)^2y^2+2y-a^2+17(x-1)^2+4(x-1)(y+2)-20(y+2)^2
问题描述:
用十字乘法因式分解,好的追加分:8x^2y^2+6xy-35 2(a+b)^2+(a+b)(a-b)-6(a-b)^2
y^2+2y-a^2+1
7(x-1)^2+4(x-1)(y+2)-20(y+2)^2
答
8x^2y^2+6xy-35
=(2x+5y)(4x-7y)
2(a+b)^2+(a+b)(a-b)-6(a-b)^2
=[2(a+b)-3(a-b)][(a+b)+2(a-b)]
=(2a+2b-3a+3b)(a+b+2a-2b)
=(5b-a)(3a-b)
y^2+2y-a^2+1
=y^2+2y+1-a^2
=(y+1)^2-a^2
=(y+1-a)(y+1+a)
7(x-1)^2+4(x-1)(y+2)-20(y+2)^2
=[(x-1)+2(y+2)][7(x-1)-10(y+2)]
=(x-1+2y+4)(7x-7-10y-20)
=(x+2y+3)(7x-10y-27)