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. - Get link 4share
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
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:
📰 kenpachi bleach 📰 kenpachi zaraki 📰 kenshi in mortal kombat 📰 Tai To Game Shock Inside The Shocking Twist That Changed Everything 📰 Tai Tos Secret Strategy Is Revolutionary Discover It Before Its Gone 📰 Tai Tos Secret Weapon The Hidden Gameplay That No One Tells You 📰 Taiga Biome Exploits Get Insane Loot Survival Tips That Will Take Your Minecraft Game To New Levels 📰 Taiga Biome Minecraft The Ultimate Survival Guide Thatll Change How You Play Forever 📰 Taiga Biome Revealed The Ultimate Survival Challenge Parents Never Prepared You For 📰 Taillez Like A Pro The Shocking Technique Anyone Struggling With Fit Needs To Try 📰 Taillow The Game Changer Redefining Your Style Forever 📰 Tailored Pants That Look Expensive But Cost Less Than Your Dream Outfit 📰 Tailored Pants Youll Lovebecause Fashion Should Fit Your Body Not The Other Way Around 📰 Taipei American School The Secret And Unexpected Secrets Of Its World Class Education 📰 Taj Mahal Countertops Revealed Stunning Marble Thats Taking Homes By Storm 📰 Taj Mahal Countertops The Rare Marble Thats Revolutionizing Modern Home Decor 📰 Taj Mahal Quartzite Just Shocked Everyone Why This Natural Wonder Is Now Trending 📰 Taj Mahal Quartzite The Hidden Gem Youre Missing On Instagrams Most Amazing Property PhotosFinal 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
