SUMMARY
The expression x^4 + 2x^2*y^2 + y^4 can be factored as the square of a binomial. By substituting u = x^2 and v = y^2, the expression transforms into (u)^2 + 2uv + (v)^2, which directly corresponds to the binomial expansion (a+b)^2 = a^2 + 2ab + b^2. Thus, the original expression factors to (x^2 + y^2)^2.
PREREQUISITES
- Understanding of polynomial expressions
- Familiarity with binomial expansion
- Knowledge of variable substitution in algebra
- Basic skills in factoring quadratic forms
NEXT STEPS
- Study polynomial factoring techniques
- Learn about binomial expansions and their applications
- Explore advanced algebraic identities
- Practice variable substitution in complex expressions
USEFUL FOR
Students studying algebra, educators teaching polynomial factoring, and anyone looking to enhance their understanding of algebraic expressions.