x^4 + ( -2x^3 + 2x^3 ) + (3x^2 - 4x^2 + 3x^2) + (6x - 6x) + 9 = x^4 + 2x^2 + 9 - Aurero
Simplifying the Polynomial: Proving That
x⁴ + (−2x³ + 2x³) + (3x² − 4x² + 3x²) + (6x − 6x) + 9 = x⁴ + 2x² + 9
Simplifying the Polynomial: Proving That
x⁴ + (−2x³ + 2x³) + (3x² − 4x² + 3x²) + (6x − 6x) + 9 = x⁴ + 2x² + 9
Mathematics often involves simplifying expressions to reveal their true form — clean, elegant, and easy to analyze. In this article, we break down one such polynomial simplification step-by-step, showing how combining like terms leads us to the simplified expression:
x⁴ + 2x² + 9
Why Simplify Polynomials?
Understanding the Context
Before diving in, it’s important to understand why simplifying polynomials matters. Simplified forms make equations easier to solve, analyze, and graph. They also reveal underlying patterns — key in algebra, calculus, and advanced math contexts.
The Given Expression
We start with:
x⁴ + (−2x³ + 2x³) + (3x² − 4x² + 3x²) + (6x − 6x) + 9
Key Insights
At first glance, it may seem complicated, but all terms contain like terms — parts of the polynomial that share the same variable powers.
Step 1: Combine the x³ Terms
Look closely at the cubic (degree 3) terms:
−2x³ + 2x³
These are like terms because both have x³:
$$
(-2 + 2)x³ = 0x³ = 0
$$
So, these terms cancel each other out:
(−2x³ + 2x³) = 0
🔗 Related Articles You Might Like:
📰 Why Everyone’s Obsessed with Charcoal Grey—Discover the Secret Behind Its Magnetic Appeal! 📰 See How Charcoal Grey Transforms Modern Interiors: A Must-Know Trend in 2024! 📰 Charcoal Grey vs. Every Other Color: Which One Will Dominate Your Space in 2025? 📰 Fracpi Rfraca B H2 Frac2Pi Ra B H 📰 Fracsin Xcos X Fraccos Xsin X Fracsin2 X Cos2 Xsin X Cos X Frac1Sin X Cos X 📰 Fracvtextspherevtexthemisphere Fracfrac43Pi R318Pi R3 Frac43 Cdot Frac118 Frac454 Frac227 📰 Fracx 2X 2 1 Quad Rightarrow Quad X 2 X 2 📰 Fracx2Y Fracy2Z Fracz2X Geq Fracx Y Z2Y Z X Frac323 3 📰 Freaky Proven Secrets To Stunning Christmas Wreaths Every Home Needs 📰 Free Winnie The Pooh Coloring Pages The Ultimate Gentlemans Guide To Cute Adventure Fun 📰 Free Wordscapes Cheats That Will Make You Win Every Puzzle Instantly 📰 Free Xbox Game Pass Ultimate Trial Swipe Below To Claim Over 100 In Games Now 📰 Free Xbox Just Dropped For Sale 4K Gaming Power In Your Hands Limited Time 📰 Fresh Unseen Facts About Women In The Bible You Need To Read Now 📰 From 20 Wings To Grado Playhere Are The Wingstop Reviews That Sold Millions 📰 From 2005 To Now The Historic Year Xbox 360 Changed Gaming Forever 📰 From Aaa Fights To Indie Gems The Ultimate Pc Game Pass Lineup You Need To See 📰 From Action Movie Magic To Real Life Discover The Iconic Womens Wonder Woman CostumeFinal Thoughts
Step 2: Combine the x² Terms
Now examine the quadratic (degree 2) terms:
3x² − 4x² + 3x²
Group like terms:
$$
(3 - 4 + 3)x² = (6 - 4)x² = 2x²
$$
Thus:
(3x² − 4x² + 3x²) = 2x²
Step 3: Combine the x Terms
Look at the linear (degree 1) terms:
6x − 6x
These are also like terms:
$$
(6 - 6)x = 0x = 0
$$
So, (6x − 6x) = 0
Step 4: Keep Constant Term
Finally, the standalone constant:
+9
