Question

Answer 1

`a,(ab-1)^2 + (a+b)^2`

`=a^2 b^2 -2ab+1 + a^2 +b^2 +2ab`

`=a^2 b^2 +a^2+1+b^2`

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

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

`b,x^3 +2x^2 +2x+1`

`=x^3 +x^2 +x^2 +x+x+1`

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

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

`c,x^2 -2x-4y^2 -4y`

`=x^2 -4y^2 -2x-4y`

`=(x-2y)(x+2y)-2(x+2y)`

`=(x+2y)(x-2y-2)`

Answer 2

a, \(\left(ab-1\right)^2+\left(a+b\right)^2=a^2b^2-2ab+1+a^2+2ab+b^2\)

\(=b^2\left(a^2+1\right)+a^2+1=\left(a^2+1\right)\left(b^2+1\right)\)

b, \(x^3+2x^2+2x+1=\left(x+1\right)\left(x^2-x+1\right)+2x\left(x+1\right)=\left(x+1\right)\left(x^2+x+1\right)\)

c, \(x^2-2x-4y^2-4y=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)=\left(x+2y\right)\left(x-2y-2\right)\)