Question: Expand the product $ (2x - 3)(x + 4)(x - 1) $. - IQnection
Expanding the Product: $ (2x - 3)(x + 4)(x - 1) $
Expanding the Product: $ (2x - 3)(x + 4)(x - 1) $
If you're working with cubic expressions in algebra, expanding products like $ (2x - 3)(x + 4)(x - 1) $ may seem tricky at first—but with the right approach, it becomes a smooth process. In this article, we’ll walk step-by-step through expanding the expression $ (2x - 3)(x + 4)(x - 1) $, explain key algebraic concepts, and highlight how mastering this technique improves your overall math proficiency.
Understanding the Context
Why Expand Algebraic Expressions?
Expanding products helps simplify expressions, solve equations, and prepare for higher-level math such as calculus and polynomial factoring. Being able to expand $ (2x - 3)(x + 4)(x - 1) $ not only aids in solving expressions but also strengthens problem-solving skills.
Step-by-Step Expansion
Image Gallery
Key Insights
Step 1: Multiply the first two binomials
Start by multiplying $ (2x - 3) $ and $ (x + 4) $:
$$
(2x - 3)(x + 4) = 2x(x) + 2x(4) - 3(x) - 3(4)
$$
$$
= 2x^2 + 8x - 3x - 12
$$
$$
= 2x^2 + 5x - 12
$$
🔗 Related Articles You Might Like:
📰 The Butterfly Dress That’s Taking Social Media by Storm—Shop Now Before It’s Gone! 📰 This Lightweight Butterfly Dress Is the Secret to Effortless Summer Glam—See Why! 📰 Dress Like a Fairy! The Butterfly Dress That’s Taking Instagram to New Heights! 📰 Size It Right Standard Window Dimensions That Change Your Homes Appeal Forever 7798346 📰 Why These Huge Fluffy Dogs Are The Cutest And Moms Favorite 813229 📰 Youll Never Guess How Easily You Can Upgrade Your Tcl Roku Tv With This Simple Remote Hack 3996976 📰 Bank Of America Pre Approval Home Loan 9803890 📰 What Is Verizon 611 8658375 📰 This Observers Mind Blowing Moment Reggie Fils Aime Confesses What No One Expected 6009431 📰 The Human Torch 3005016 📰 Mcforman 2281731 📰 This New Expansion In Vampire The Masquerade Has Everyone Obsessed Over Bloodlines 2 621716 📰 Powerball Ri 3821618 📰 5 Experts Weigh In Moneylion Stock Discussion Proving Its The Next Mega Opportunity 8075604 📰 Current Debit Card 9855059 📰 Picture Ids In Roblox 2651526 📰 Cute Backgrounds Aesthetic 9109360 📰 Sturbridge Host Hotel 2298115Final Thoughts
Step 2: Multiply the result by the third binomial
Now multiply $ (2x^2 + 5x - 12)(x - 1) $:
Use the distributive property (also known as FOIL for binomials extended to polynomials):
$$
(2x^2 + 5x - 12)(x - 1) = 2x^2(x) + 2x^2(-1) + 5x(x) + 5x(-1) -12(x) -12(-1)
$$
$$
= 2x^3 - 2x^2 + 5x^2 - 5x - 12x + 12
$$
Step 3: Combine like terms
Now combine terms with the same degree:
- $ 2x^3 $
- $ (-2x^2 + 5x^2) = 3x^2 $
- $ (-5x - 12x) = -17x $
- Constant: $ +12 $
