-6t^2(2t - t^4) = -12t^3 + 6t^6. - AdVision eCommerce
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:
📰 Update Naar Windows 10 📰 Update Network Adapter Driver 📰 Update Network Drivers 📰 The Shocking Truth Full Liquid Diet Burns Fat Faster Than You Think 8552358 📰 Jaycee Tekken 2240836 📰 Actor Moe Howard Shocked Fans With This Untold Historical Revelation 668910 📰 Apt For Rent Plant City Fl 2723031 📰 Stop Wasting Time This One Rule Unlocks Absolute Range Every Time 3102990 📰 Epic Games Discord Nitro 6142479 📰 Gg Xrd Rev 2 2896719 📰 Alineaciones De Torino Fc Contra Ac Milan 1820268 📰 Rurouni Kenshin Manga The Shot In The Dark Moments That Made Us All Fall In Love 5465134 📰 What Type Of Water For Formula 6077416 📰 Allegany College Of Maryland 6790218 📰 Battle Net Downloader 442852 📰 Master Instagram Success With Instatikstop Guessing Start Succeeding 581507 📰 Identification Needed To Fly 6981091 📰 Uec Stock Price Jumped Over 300 Heres What It Means For Investors Now 6481514Final 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.
