Question

Answer 1

g.

$x^5+x+1=(x^5-x^2)+(x^2+x+1)$

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

$=(x^2+x+1)[x^2(x-1)+1]$

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

h.

$64x^4+81=(8x^2)^2+9^2+2.8x^2.9-144x^2$

$=(8x^2+9)^2-(12x)^2=(8x^2+9-12x)(8x^2+9+12x)$

i.

$16-x^2+2xy-y^2=16-(x^2-2xy+y^2)$

$=4^2-(x-y)^2=(4-x+y)(4+x-y)$

 

Answer 2

k.

$x^2-4xy+4y^2-4=(x^2-4xy+4y^2)-4=(x-2y)^2-2^2=(x-2y-2)(x-2y+2)$
m.

$4x^2-y^2+8(y-2)$

$=4x^2-y^2+8y-16$

$=4x^2-(y^2-8y+16)=(2x)^2-(y-4)^2$

=$(2x-y+4)(2x+y-4)$

n.

$3x^2-6xy+3y^2-12z^2=3(x^2-2xy+y^2-4z^2)$

$=3[(x-y)^2-(2z)^2]=3(x-y-2z)(x-y+2z)$