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We want to factor the following expression:
81x^6– (y+1)^2
We can factor the expression as (U +V)(U-V) where U and V are either constant integers or single-
variable expressions.
1) What are U and V?

Respuesta :

absor201

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]

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