Question: Expand the product $ (2x - 3)(x + 4)(x - 1) $. - Decision Point
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:
📰 Fidelity Hardship Withdrawal Form: Uncover the Truth About Hidden Fees & Delays! 📰 Stop Paying More—How the Fidelity Hardship Withdrawal Form Could Be Sabotaging You! 📰 You Cant Afford to Ignore Fidelity Forms—Heres What You Need to Know! 📰 Microsoft Photo Editor Windows 10 1126648 📰 Mind Blowing Marcus Aurelius Quotes That Every Leader And Thinker Needs To Read Now 6807084 📰 Test Your Sesame Street Fame Name These Beloved Characters In 60 Seconds 1007065 📰 The Shocking Truth Behind How This Followers Tracker Counts Every Single Follow 6813189 📰 Ree Games Revelation The Secret Mechanics Behind The Hottest Title Today 5902984 📰 Find The Cheapest Online Term Life Insurance Quotesprotect Your Family Without Waiting 8144758 📰 Best Hulu Shows 4320023 📰 Github Mac Download 2550774 📰 The Angles Are 2X 40Circ 3X 60Circ 4X 80Circ 666713 📰 Ready To Garden Here Are The Top Seeds You Need To Try Right Away 6008782 📰 Wanted English Movie 7290219 📰 Bank Of America In Sierra Vista 262523 📰 Baltimores Directions 4770408 📰 How An Easy 1 2 Switch Switch Transformed My Homewatch Now 3844684 📰 Bro Acts Like A Starbut This Team Proves Hes Not Even Closer Than The Bench 9175391Final 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 $
