-6t^2(2t - t^4) = -12t^3 + 6t^6. - Parker Core Knowledge
Simplifying and Verifying the Expression: A Comprehensive Guide to –6t²(2t – t⁴) = –12t³ + 6t⁶
Simplifying and Verifying the Expression: A Comprehensive Guide to –6t²(2t – t⁴) = –12t³ + 6t⁶
When reducing algebraic expressions or verifying equation equivalences, clear step-by-step manipulation is key. One such expression—–6t²(2t – t⁴)—often appears in algebra students’ practice, and understanding its expansion and simplification is essential for mastering polynomial manipulation. This article breaks down the equation –6t²(2t – t⁴) = –12t³ + 6t⁶ thoroughly, showing how to simplify the left-hand side and verify its equivalence with the right-hand side.
Understanding the Context
What Is the Equation?
We aim to confirm whether:
–6t²(2t – t⁴) = –12t³ + 6t⁶
This involves multiplying the binomial inside the parentheses by the polynomial outside and collecting like terms, then comparing with the given right-hand side.
Image Gallery
Key Insights
Step 1: Distribute the Polynomial
Start by distributing –6t² across each term inside the parentheses:
–6t²(2t – t⁴) = (–6t²)(2t) + (–6t²)(–t⁴)
Now calculate each product:
- (–6t²)(2t) = –12t³
- (–6t²)(–t⁴) = +6t⁶ (because a negative times a negative is positive)
🔗 Related Articles You Might Like:
📰 Your Phone Needs This Flower Wallpaper – Why Mindless Scrolling Just Got Prettier! 📰 Rave-Worthy Flower Wallpapers That Boost Your Aesthetic – Don’t Miss These Hottest Trends! 📰 "Flower Sea 2025: The Breathtaking Ocean Bloom Swarm You Won’t Believe Is Happening! 📰 Inside The Wells Fargo Stock Discussion Are Experts Predicting A Comeback 1020503 📰 Book In The Magicians 7188525 📰 Why The Ir Examiners Latest Tips Are Changing Ir Exam Success Forever 1946789 📰 Heart Gold And Soul Silver Pokemon 2692913 📰 International Money Transfer Services 2426237 📰 Unlock Instant Access To Your Wells Fargo Accountclick To See How 1768113 📰 Kissinger 5164456 📰 Tingo Bingo 4054257 📰 Puzzledom Free 4886554 📰 Wood Crown Molding 3398633 📰 Barbell Pressure Unleashed The Horrifying Truth Behind Pressure Limits 8464632 📰 Shged Not At Alltransform Your Hair In Surprising Months 7695912 📰 Jugar Roblox 9701741 📰 Escola 9914798 📰 Gun Laws Japan 5747179Final Thoughts
Step 2: Combine Like Terms
Adding the two results:
–12t³ + 6t⁶
So, the left-hand side simplifies to:
–6t²(2t – t⁴) = –12t³ + 6t⁶
Step 3: Verify Equivalence
Now observe that:
Left-hand side (LHS): –6t²(2t – t⁴) → after expansion: –12t³ + 6t⁶
Right-hand side (RHS): –12t³ + 6t⁶
Both sides are identical. Therefore, the original equation holds true.
