Understanding the Equation: 3(x² - 2x + 3) = 3x² - 6x + 9

When studying algebra, one of the most fundamental skills is simplifying and verifying equations—a process that reinforces understanding of distributive properties, factoring, and polynomial expansion. A common example that demonstrates these principles is the equation:

3(x² - 2x + 3) = 3x² - 6x + 9

Understanding the Context

This seemingly simple equation serves as a perfect illustration of the distributive property and serves as a model for checking equivalence between expressions. In this SEO-optimized article, we’ll explore step-by-step how to expand, simplify, and verify this equation, providing clear insights for students, teachers, and self-learners seeking to improve their algebraic fluency.

What Is the Equation 3(x² - 2x + 3) = 3x² - 6x + 9?

At first glance, the equation presents a linear coefficient multiplied by a trinomial expression equal to a fully expanded quadratic trinomial. This form appears frequently in algebra when students learn how to simplify expressions and verify identities.

3(x^2 - 2x + 3) = 3x^2 - 6x + 9

Key Insights

Left side: 3(x² - 2x + 3)
Right side: 3x² - 6x + 9

This equation is not just algebraic practice—it reinforces the distributive property:
a(b + c + d) = ab + ac + ad

Understanding this process helps students master more complex algebra, including factoring quadratic expressions and solving equations.

Step-by-Step Expansion: Why It Matters

Continue Reading

All match. Thus, even if not strictly cubic, $ p(0) = 0 $.
But perhaps we misread—maybe the problem says cubic but the data forces lower degree. Since the interpolation is unique, and the values sit on a quadratic, the answer is still $ p(0) = 0 $.
Alternatively, suppose we assume $ p(x) $ is cubic: $ p(x) = ax^3 + 2x^2 + x $. Then $ p(1) = a + 2 + 1 = 3 \Rightarrow a = 0 $. So $ a = 0 $, same result.

🔗 Related Articles You Might Like:

📰 sandal heels 📰 sandalphon 📰 sandals for women with platform 📰 Shocking Sombra Overwatch Secrets Revealed You Wont Believe What Shes Capable Of 📰 Shocking Story How This Son Became The Ultimate Servant To His Beloved Father 📰 Shocking Study Reveals Sleepmor Mattresses Sleep 50 Better Than Competitorstry Them Now 📰 Shocking Styles In Mens Running Shorts You Need To See 📰 Shocking Survival Horror Details Revealed In Silent Hill Wiiare You Ready To Enter 📰 Shocking Taste Bomb 5 Surprising Reasons Siracha Sauce Is A Must Have 📰 Shocking Tech Hiding In Snake Eater Metal Gear How To Get Your Hands On It Now 📰 Shocking Tips Inside The Ultimate Slot Slot Game Guide 📰 Shocking To See These Silver Chains For Menyour Wardrobe Needs Them 📰 Shocking Transformation Werewolf Secrets Thatll Blow Your Mind In Skyrim 📰 Shocking Trick Revealed The Ultimate Stylish No Show Sock Game 📰 Shocking Trick To Lock Out Bugs Without A Doordiscover The Sliding Screen Door 📰 Shocking Truth About Levis 501 Shorts Everyones Trying But You Need To See 📰 Shocking Truth About Shee Vaneer Shrine That Makes Believers Rave Online 📰 Shocking Truth About Solid Surface Countertops That Every Homeowner Should Know

Final Thoughts

To verify that both sides are equivalent, we begin with expansion:

Left Side:
3 × (x² - 2x + 3)
= 3×x² + 3×(-2x) + 3×3
= 3x² - 6x + 9

This matches the right side exactly.

Why This Step Is Crucial

Expanding ensures that both expressions represent the same polynomial value under every x. Misreading a sign or missing a coefficient can lead to incorrect conclusions—making expansion a foundational step in equation verification.

Verifying Equality: Confirming the Identity

Now that both sides expand to 3x² - 6x + 9, we conclude:

3(x² - 2x + 3) = 3x² - 6x + 9
✔️ True for all real values of x

This means the equation represents an identity—true not just for specific x-values, but across the entire real number line.