Answer:
We have [tex]\mathbf{U= 9x^3 \:and\:V=y+1}[/tex]
Step-by-step explanation:
We want to factor the expression [tex]81x^6-(y+1)^2[/tex] in the form of (U+V)(U-V)
We need to find U and V
We can use formula : [tex]a^2-b^2=(a+b)(a-b)[/tex]
We can write [tex]81x^6[/tex] as [tex](9x^3)^2[/tex]
Now we have the expression:
[tex]81x^6-(y+1)^2\\=(9x^3)^2-(y+1)^2[/tex]
Applying formula: [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]=(9x^3+y+1)(9x^3-(y+1))\\=(9x^3+y+1)(9x^3-y-1)[/tex]
So, we have [tex]\mathbf{U= 9x^3 \:and\:V=y+1}[/tex]
