Question

We want to factor the following expression:

16x^4-(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.

photo:
1) What are U and V?
2)Factor the expression.​

Answer 1

Explanation:

`16x^4-(y-1)^2=4^2\cdot (x^2)^2-(y-1)^2=(\textcolor{blue}{4x^2})^2-(\textcolor{green}{y-1})^2`

`\text{Comparing with } \textcolor{blue}{U}^2-\textcolor{green}{V}^2, \text{ we know}`

`\textcolor{red}{U=4x^2, V=(y-1)}`

`\text{By the formula } U^2-V^2=(U+V)(U-V)`

`16x^4-(y-1)^2=(4x^2)^2-(y-1)^2=\textcolor{red}{(4x^2+y-1)(4x^2-y+1)}`