Question: Expand the product $ (2x - 3)(x + 4)(x - 1) $. - AIKO, infinite ways to autonomy.
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:
📰 How many positive 3-digit numbers are divisible by 11? 📰 Now, count the multiples of 11 from 110 to 990 inclusive: 📰 The square root of a square gives the absolute value: 📰 Removal Of Anus Skin Tags 1114127 📰 Stop Waiting Discover The Ultimate Emergency Chat App That Saves Lives 5226227 📰 Yeezy Red October The Secret Drop That Shocked Sneakerheads This October 3348978 📰 New Digimon Game Storms The Market What Secret Power Will Change Battles Forever 7648405 📰 Why Todays Carnival Stock Price Is Soaring Way Beyond Expectationsbuy Now 374114 📰 Setting The Discriminant Equal To Zero For Exactly One Real Root We Have 6625193 📰 How I Became The Paintball King Pro Tips You Need To See 233742 📰 Sgx Nio Magic Uncovering The Game Changer Behind Next Level Speed Power 8403870 📰 Youll Never Guess How The Bloom App Helps You Grow Instantlytry It Now 9160587 📰 Master Indenting Paragraphs In Word Faster Than You Thinktry These Simple Steps 7524 📰 Apple Tv Shows To Watch 1636029 📰 How The Rays Drove The Padres To The Brink Of Collapse 8694179 📰 Enacted Synonym 4563068 📰 Clarity App Shocked Meits The Secret To Sharper Focus Better Productivity 1371397 📰 Sarku Near Me 5717650Final 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 $
