f.2 factorization~~~(15點)

1.-4n2+25p2
=25p2-4n2
=(5p-2n)(5p+2n)


2.(a-5)2-(b+3)2
=[(a-4)-(b+3)][(a-4)+(b+3)]
=(a-b-7)(a+b-1)

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

4.(c+d)2-9(2d-c)2
=[(c+d)-3(2d-c)][(c+d)+3(2d-c)]
=(4c-5d)(-2c+7d)

5.n2+3n+3p-p2
=n2-p2+3n+3p
=(n-p)(n+p)+3(n+p)
=(n+p)(n-p+3)

1.-4n2+25p2



=25p2-4n2



=(5p-2n)(5p+2n)





2.(a-5)2-(b+3)2



=[(a-4)-(b+3)][(a-4)+(b+3)]



=(a-b-7)(a+b-1)




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



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



=(-a-3b)(3a-b)



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







4.(c+d)2-9(2d-c)2



=[(c+d)-3(2d-c)][(c+d)+3(2d-c)]



=(4c-5d)(-2c+7d)







5.n2+3n+3p-p2



=n2-p2+3n+3p



=(n-p)(n+p)+3(n+p)



=(n+p)(n-p+3)

1.-4n^2 + 25p^2
= (5p)^2 - (2n)^2
= (5p + 2n)(5p - 2n)
2. (a - 5)^2 - (b + 3)^2
= (a - 5 + b + 3)(a - 5 - b - 3)
= (a + b - 2)(a - b - 8)
3.(a - 2b)^2 - (2a + b)^2
= (a - 2b + 2a + b)(a - 2b - 2a - b)
= (3a - b)(-a - 3b)
= (b - 3a)(a + 3b)
4.(c + d)^2 - 9(2d - c)^2
= (c + d)^2 - (6d - 3c)^2
= (c + d + 6d - 3c)(c + d - 6d + 3c)
= (7d - 2c)(4c - 5d)
5. n^2 + 3n + 3p - p^2
= n^2 + 3n + 9/4 - 9/4 + 3p - p^2
= (n + 3/2)^2 - (p - 3/2)^2
= (n + 3/2 + p - 3/2)(n + 3/2 - p + 3/2)
= (n + p)(n - p + 3)
Alternatively,
n^2 + 3n + 3p - p^2
= n^2 - p^2 + 3n + 3p
= (n - p)(n + p) + 3(n + p)
= (n - p + 3)(n + p)