Factorize (F.2 )

1) (x+2y)2﹣(3x﹣y)2
= [(x+2y)﹣(3x﹣y)][(x+2y)+(3x﹣y)]
= (x+2y﹣3x+y)(x+2y+3x﹣y)
= (﹣2x+3y)(4x+y)
= ﹣(2x﹣3y)(4x+y)

2) (4x﹣5y)2﹣(5x﹣4y)2
= [(4x﹣5y)﹣(5x﹣4y)][(4x﹣5y)+(5x﹣4y)]
= (4x﹣5y﹣5x+4y)(4x﹣5y+5x﹣4y)
= (﹣x﹣y)(9x﹣9y)
= ﹣(x+y)9(x﹣y)
= ﹣9(x﹣y)(x+y)

3) (a+b)2﹣2(a+b)+1
= [(a+b)﹣1]2
= (a+b﹣1)2

4) 2(x﹣y)2+8(x﹣y)+8
= 2[(x﹣y)2+4(x﹣y)+4]
= 2[(x﹣y)+2]2
=2(x﹣y+2)2

第1和2題應用了恆等式a2﹣b2= (a﹣b)(a+b)
第3和4題應用了恆等式(a+b)2= a2+2ab+b2