Expansion Intuition Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Expand (2x−3)2(2x - 3)^2.

Solution

  1. 1
    Apply the perfect square pattern: (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2.
  2. 2
    Here a=2xa = 2x and b=3b = 3.
  3. 3
    (2x)2−2(2x)(3)+32=4x2−12x+9(2x)^2 - 2(2x)(3) + 3^2 = 4x^2 - 12x + 9.

Answer

4x2−12x+94x^2 - 12x + 9
The perfect square trinomial pattern avoids the full FOIL computation. A common mistake is writing (2x−3)2=4x2−9(2x-3)^2 = 4x^2 - 9, which forgets the middle term −12x-12x.

About Expansion Intuition

Understanding algebraic expansion as the process of applying the distributive property to multiply out factors and remove parentheses.

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More Expansion Intuition Examples

Example 1 easy

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Example 3 easy

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Example 4 medium

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