Absolutely, let's break down the expression step-by-step.
We are given the expression:
[tex]\[ x^4 + 7x^2y^2 + 16y^4 \][/tex]
To proceed, let's consider the following steps:
1. Identify the Components:
- The term [tex]\( x^4 \)[/tex] is a pure fourth power of [tex]\( x \)[/tex].
- [tex]\( 7x^2y^2 \)[/tex] involves both [tex]\( x \)[/tex] and [tex]\( y \)[/tex] and is a product of squares, specifically [tex]\( (x^2)(y^2) \)[/tex], scaled by 7.
- [tex]\( 16y^4 \)[/tex] is a pure fourth power of [tex]\( y \)[/tex], scaled by 16.
2. Expand and Simplify:
- Note that in this expression, each term is already fully expanded and simplified to its simplest form.
- There are no hidden factorizations or simplifications for the given terms that can further reduce the expression.
Therefore, the final expanded form of the expression [tex]\( x^4 + 7x^2y^2 + 16y^4 \)[/tex] is:
[tex]\[ \boxed{x^4 + 7x^2y^2 + 16y^4} \][/tex]
This is the simplest form we can write for this expression, and there are no further calculations or simplifications needed.
