3(x^6 - 6x^4 + 12x^2 - 8) - 22(x^4 - 4x^2 + 4) + 57x^2 - 114 - 52 = 3x^6 - 18x^4 + 36x^2 - 24 - 22x^4 + 88x^2 - 88 + 57x^2 - 166 = 3x^6 - 40x^4 + 181x^2 - 278. - RoadRUNNER Motorcycle Touring & Travel Magazine
Simplifying 3(x⁶ - 6x⁴ + 12x² - 8) - 22(x⁴ - 4x² + 4) + 57x² - 114 - 52: A Step-by-Step Simplification
Simplifying 3(x⁶ - 6x⁴ + 12x² - 8) - 22(x⁴ - 4x² + 4) + 57x² - 114 - 52: A Step-by-Step Simplification
Simplifying polynomial expressions can often feel like solving a puzzle—especially when nested parentheses, coefficients, and multiple terms are involved. In this article, we’ll break down the complex expression:
3(x⁶ - 6x⁴ + 12x² - 8) - 22(x⁴ - 4x² + 4) + 57x² - 114 - 52
and simplify it step by step to arrive at the final form:
3x⁶ - 40x⁴ + 181x² - 278
Understanding the Context
Why Simplifying Matters
Working with polynomials is essential across mathematics, engineering, computer science, and data analysis. Simplifying expressions reduces errors, improves readability, and makes it easier to analyze behavior—critical when solving equations, plotting graphs, or optimizing functions.
Step 1: Expand Each Bracketed Term
Image Gallery
Key Insights
The expression contains three main parts with parentheses:
- 3(x⁶ - 6x⁴ + 12x² - 8)
- -22(x⁴ - 4x² + 4)
- +57x² - 114 - 52 (constant terms)
To simplify, we start by expanding the first two polynomial brackets.
Expanding 3(x⁶ - 6x⁴ + 12x² - 8)
Multiply each term inside the parentheses by 3:
= 3·x⁶ - 18x⁴ + 36x² - 24
= 3x⁶ - 18x⁴ + 36x² - 24
🔗 Related Articles You Might Like:
📰 movies like the notebook 📰 movies man of steel 📰 movies michelle rodriguez 📰 Critical Evidence Tech Coach Verizon Wireless And It Sparks Debate 📰 Kim Kardashian Tape 6832986 📰 What Does Amortization Mean 📰 Irish Republic Capital 5071845 📰 Best Skinny Mens Wallet 📰 Ecu Acceptance Rate 5893789 📰 Combined They Read 25 15 40 Pages Per Day 2441265 📰 Home Loan Rate Today 6630235 📰 Roblox Classic Clothes Maker 📰 Play Fancy Pants 📰 How Long Does Poison Ivy Take To Show Up 9534885 📰 What Is A Chro 📰 Love After The Apocalypse The Most Romantic Story To Break Your Heart So You Wont 9135107 📰 Induction Vs Electric Stove 📰 The Pike Pushup Hack That Powers Up Your Upper Body Overnight 5541128Final Thoughts
Expanding -22(x⁴ - 4x² + 4)
Multiply each term by -22:
= -22x⁴ + 88x² - 88
Step 2: Combine All Expanded Terms
Now replace the original grouped expressions with their expanded forms:
Original expression becomes:
(3x⁶ - 18x⁴ + 36x² - 24) + (-22x⁴ + 88x² - 88) + 57x² - 114 - 52
Combine like terms:
- x⁶ term: only 3x⁶ (no other x⁶ terms)
- x⁴ terms: -18x⁴ - 22x⁴ = -40x⁴
- x² terms: 36x² + 88x² + 57x² = (36 + 88 + 57)x² = 181x²
- Constant terms: -24 - 88 - 114 - 52
Calculate constants:
-24 - 88 = -112
-112 - 114 = -226
-226 - 52 = -278
Final Simplified Expression
Putting it all together:
3x⁶ - 40x⁴ + 181x² - 278
