Question: Expand the product $ (2x - 3)(x + 4)(x - 1) $. - Treasure Valley Movers

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.

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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.

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Step-by-Step Expansion

Step 1: Multiply the first two binomials

Start by multiplying $ (2x - 3) $ and $ (x + 4) $:

$$
(2x - 3)(x + 4) = 2x(x) + 2x(4) - 3(x) - 3(4)
$$

$$
= 2x^2 + 8x - 3x - 12
$$

$$
= 2x^2 + 5x - 12
$$

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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):

$$
(2x^2 + 5x - 12)(x - 1) = 2x^2(x) + 2x^2(-1) + 5x(x) + 5x(-1) -12(x) -12(-1)
$$

$$
= 2x^3 - 2x^2 + 5x^2 - 5x - 12x + 12
$$

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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 $