=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