Question

We want to factor the following expression:

Answer 1

Answer:

We have $\mathbf{U= 9x^3 \:and\:V=y+1}$

Step-by-step explanation:

We want to factor the expression $81x^6-(y+1)^2$ in the form of (U+V)(U-V)

We need to find U and V

We can use formula : $a^2-b^2=(a+b)(a-b)$

We can write $81x^6$ as $(9x^3)^2$

Now we have the expression:

$81x^6-(y+1)^2\\=(9x^3)^2-(y+1)^2$

Applying formula: $a^2-b^2=(a+b)(a-b)$

$=(9x^3+y+1)(9x^3-(y+1))\\=(9x^3+y+1)(9x^3-y-1)$

So, we have $\mathbf{U= 9x^3 \:and\:V=y+1}$