=abc^2+abd^2+a^2cd+b^2cd

=(abc^2+a^2cd)+(abd^2+b^2cd)

=ac (BC+AD) +bd (BC+AD)

=(bc+ad)(ac+bd)

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

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

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

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

=2b(b-a)

3 . x(x- 1)+y(y+ 1)-2xy

=x^2-x+y^2+y-2xy

=(x-y)^2-(x-y)

=(x-y)(x-y- 1)

4.(c^2-b^2+d^2-a^2)^2-4(ab-od)^2

=[(c^2-b^2+d^2-a^2)+2(ab-cd)][(c^2-b^2+d^2-a^2)-2(ab-od)]

=(c^2-b^2+d^2-a^2+2ab-2cd)(c^2-b^2+d^2-a^2-2ab+2cd)

=[(c-d)^2-(a-b)^2][(c+d)^2-(a+b)^2]

=(c-d-a+b)(c-d+a-b)(c+d+a+b)(c+d-a-b)

5.a^4+2a^3+3a^2+2a+ 1

=(a^4+2a^2+ 1)+(2a^3+2a)+a^2

=(a^2+ 1)^2+2a(a^2+ 1)+a^2

=(a^2+ 1+a)^2

6.x^3-7x+6

=(x^3- 1)-7x+7

=(x- 1)(x^2+x+ 1)-7(x- 1)

=(x- 1)(x^2+x+ 1-7)

=(x- 1)(x^2+x-6)

=(x- 1)(x-2)(x+3)

7.a^2-20a+64

=(x-4)(x- 16)

8.(x^4+2)^2-9x^4

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

=(x^2+ 1)(x^2+2)(x^2- 1)(x^2-2)

=(x^2+ 1)(x^2+2)(x+ 1)(x- 1)(x^2-2)

9.a^2-b^2+4a+2b+3

=(a^2+4a+4)-(b^2-2b+ 1)

=(a+2)^2-(b- 1)^2

=(a+2+b- 1)(a+2-b+ 1)

=(a+b+ 1)(a-b+3)

10.(x^2+4)^2+3x(x^2+4)+2x^2

=(x^2+4+2x)(x^2+4+x)

1 1.(x^2+3x-2)(x^2+3x+4)- 16

=[(x^2+3x)-2][(x^2+3x)+4]- 16

=(x^2+3x)^2+2(x^2+3x)-8- 16

=(x^2+3x)^2+2(x^2+3x)-24

=(x^2+3x+6)(x^2+3x-4)

=(x^2+3x+6)(x+4)(x- 1)

12.(x+ 1)(x+2)(x+3)(x+4)+ 1

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

=[(x^2+5x)+4][(x^2+5x)+6]+ 1

=(x^2+5x)^2+ 10(x^2+5x)+24+ 1

=(x^2+5x)^2+ 10(x^2+5x)+25

=(x^2+5x+5)^2