1) 3x2-12y2=3(x2-4y2)=3(x-2y)(x+2y)
2)5xy2-10xyz+5xz2=5x(y2-2yz+z2)=5x(y-z)2
3)x3+3x2+3x+1-27x3=(x+1)3-(3x)3=(-2x+1)(x2+2x+2+3x2+3x+9x2)
=(-2x+1)(13x2+5x+2)
4)9(x+5)2-(x-7)2=(3x+15)2-(x-7)2=(2x+22)(4x+8)=8(x+11)(x+2)
5)25(x-y)2-16(x+y)2=(5x-5y)2-(4x+4y)2=(x-9y)(9x-y)
6)x4+4x2-5=(x4+5x2)-(x2+5)=x2(x2+5)-(x2+5)=(x2-1)(x2+5)
=(x-1)(x+1)(x2+5)
7)x4+x2+1=(x4-x)+(x2+x+1)=x(x3-1)+(x2+x+1) =x(x-1)(x2+x+1)-(x2+x+1)=(x2+x+1)(x2-x-1)
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