The Lazy Way to dismantle fourth degree polynomial monster taming
Автор: Trick=Treat
Загружено: 2025-12-30
Просмотров: 110
Welcome to Trick=Treat! In this video, we dismantle a monstrous algebra expression: (x + 2)⁴ + (x + 4)⁴ – 706.
At first glance, your instinct might be to use "brute force" and expand these binomials. But expanding to the fourth power is messy, painful, and prone to errors. Instead, we are going to use a powerful tool called Symmetry (or the Average Method).
By introducing a change of variable (u-substitution) based on the average of the terms, we can make the odd powers cancel out perfectly, turning a nightmare calculation into an elegant biquadratic equation.
In this video, you will learn:
Why you should avoid expanding high-degree polynomials.
How to find the axis of symmetry in algebraic expressions.
How to use u-substitution to simplify quartic equations.
Techniques for factoring biquadratic polynomials.
#MathTricks #Algebra #Polynomials #TrickEqualsTreat #MathOlympiad
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