x^4 + ( -2x^3 + 2x^3 ) + (3x^2 - 4x^2 + 3x^2) + (6x - 6x) + 9 = x^4 + 2x^2 + 9 - RoadRUNNER Motorcycle Touring & Travel Magazine
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
Image Gallery
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:
📰 jamaica all-inclusive resorts adults only 📰 spring break spots 📰 gflight 📰 Shell Recharge Charging Station The Secret Weapons Keeping Your Phone Powered All Day 6363408 📰 Lo Que Prohibieron Los Networkes Y Por Qu Llegan Noticias Falsas 6481220 📰 Wordle Answer Feb 18Th 📰 Politoed Energy How To Dominate Every Conversation Like A Profast 7554479 📰 Stanton Pa 3168749 📰 1St National Bank Of Scotia 626742 📰 Netflix Tudum 2025 3812198 📰 Current Chiefs Game Score 579222 📰 How To Redeem V Bucks On Switch 📰 Discover Why Blanco By Nature Changed My Entire Wardrobe Forever 2172807 📰 Why 750 Ml Isnt Just Waterunlock The Hidden Ounces And Speak The Truth About Measurement 7793041 📰 Superhero Body Roblox 📰 Until Dawn Remake 📰 Malcolm Sayer Doctor 📰 Text To Numbers In ExcelFinal 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
