Problem
ALG-B1-M01-P001 Hidden Difference of Squares
#1
★☆☆☆☆ Level 1 of 5
Factor \( (x^2+2x+3)^2-(x^2-3)^2 \).
Denote the two large expressions by \(U\) and \(V\), then use \(U^2-V^2\).
Let \(U=x^2+2x+3\), \(V=x^2-3\). The expression equals \((U-V)(U+V)\).
We have \(U-V=2x+6=2(x+3)\), \(U+V=2x^2+2x=2x(x+1)\). Hence the factorization is \(4x(x+1)(x+3)\).
Checks basic recognition of \(U^2-V^2\).