Question

请把下列各式分解因式，谢谢

(2a+b)²-(a-2b)²
a²c-abd-abc+a²d
(a-2b)²+(a-2b)-12
2(x-y)²z²-4(x-y)z²-48z²
81(x+y)的四次方-16(x-y)的四次方
(ax+by)²-(bx+ay)²
m的四次方-2(m²-½).

Answer 1

(2a+b)²-(a-2b)²
=(2a+b-a+2b)(2a+b+a-2b)
=(a+3b)(2a-b)

a²c-abd-abc+a²d
=ac(a-b)+ad(a-b)
=a(a-b)(c+d)

(a-2b)²+(a-2b)-12
=(a-2b+3)(a-2b-4)

2(x-y)²z²-4(x-y)z²-48z²
=2z²[(x-y)²-2(x-y)-24]
=2z²(x-y+4)(x-y-6)

81(x+y)的四次方-16(x-y)的四次方
=[9(x+y)²-4(x-y)²][9(x+y)²+4(x-y)²]
=(3x+3y-2x+2y)(3x+3y+2x-2y)(9x²+18xy+9y²+4x²-8xy+4y²)
=(x+5y)(5x+y)(13x²+10xy+13y²)

(ax+by)²-(bx+ay)²
=(ax+by-bx-ay)(ax+by+bx+ay)
=[x(a-b)-y(a-b)][x(a+b)+y(a+b)]
=(a-b)(x-y)(a+b)(x+y)

m的四次方-2(m²-½)
=m^4-2m+1
=(m²-1)²
=(m-1)²(m+1)²