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. - Londonproperty
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:
📰 Upgrade Your Lifestyle: Luxurious 2 Bedroom 2 Bath Apartments That Sell in Hours! 📰 A rectangle has a length that is 3 times its width. If the width is 4 meters, find the perimeter of the rectangle. 📰 Let the width be \( w = 4 \) meters. 📰 40 Festive Flavored The Most Clickbait Infused Happy 40Th Birthday Countdown 📰 40 Years Young Still Happy Heres The Best Surprise Birthday Surprise Youll Love 📰 43 16X 📰 44 Secrets Revealed In Harry Potter In 5 Youll Want To Watch Every Clue 📰 450M Views Hello Kitty Girl Meme Explodes Online Why Its Going Viral 📰 4Download Now The Epic Story Behind Gurren Laggans Legendary Climax 📰 4Haircare Hub Master These 5 Braided Hairstyles For Maximum Flexibility Flair 📰 4Happy Birthday Magic Scroll To View The Most Heavenly Images That Will Make You Smile 📰 4Havoc Movie Spoiler Shock The Ending Left Fans Speechlesswhy Is Everyone Obsessed 📰 4Heart Gif Trends The Wildly Viral Clip You Need On Your Socials Today 📰 4Seo Hisuian Arcanine Revealed The Secret Strength Behind Legendary Beasts 📰 4Seo Top 10 Happy Birthday Coloring Pages Free Printable Happy Birthday Coloring Pages 📰 4Stop Guessing Find Your True Hair Type With Our Fast Expert Hair Quiz 📰 4X 3 2 4X 12 📰 4X 48Final 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
