Question

数学因式分解题（用平方差公式）！急！！过程！

①x²-（y-1）²
②-1+（m-1）²
③(2x+y)²-(2x-3y)²
④25(x-y)²-(x+y)²
⑤9(m+n)²-4(2m-n)²
⑥（x-y+z）²-(x-y-z)²
⑦198²-202²

Answer 1

①x²-（y-1）²
=（x+y-1）(x-y+1)

②-1+（m-1）²
=(m-1+1)(m-1-1)
=m(m-2)

③(2x+y)²-(2x-3y)²
=(2x+y+2x-3y)(2x+y-2x+3y)
=4y(4x-2y)

④25(x-y)²-(x+y)²
=(5(x-y)+x+y)(5(x-y)-x-y)
=(6x-4y)(4x-6y)

⑤9(m+n)²-4(2m-n)²
=(3(m+n)+2(2m-n))(3(m+n)-2(2m-n))
=(3m+3n+4m-2n)(3m+3n-4m+2n)
=(7m+n)(5n-m)

⑥（x-y+z）²-(x-y-z)²
=（x-y+z+x-y-z)(x-y+z-x+y+z)
=2z(2x-2y)
=4z(x-y)

⑦198²-202²
=(200-2)²-(200+2)²
=(200-2+200+2)(200-2-200-2)
=400×(-4)
=-1600