\(a,x\left(x+y\right)+6x+6y=x\left(x+y\right)+6\left(x+y\right)=\left(x+y\right)\left(x+6\right)\\ b,x^2-2x-4y^2+1=\left(x^2-2x+1\right)-4y^2=\left(x-1\right)^2-\left(2y\right)^2=\left(x-2y-1\right)\left(x+2y-1\right)\\ c,x\left(x-y\right)+4x-4y=x\left(x-y\right)+4\left(x-y\right)=\left(x-y\right)\left(x+4\right)\\ d,a^2+2a-b^2+1=\left(a^2+2a+1\right)-b^2=\left(a+1\right)^2-b^2=\left(a+b+1\right)\left(a-b+1\right)\)
a) x(x+y)+6x+6y
= x(x+y)+6(x+y)
= (x+6)(x+y)
b) x2-2x-4x2+1
= (x2-2x+1)-(2x)2
= (x-1)2-(2x)2
= (x-1-2x)(x-1+2X)
c) x(x-y)+4x-4y
= x(x-y)+4(x-y)
= (x+4)(x-y)
d) a2+2a-b2+1
= (a2+2x+1)-b2
= (x+1)2-b2
= (x+1-b)(x+1+b)
