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(x+2)(x-2)(x+3)(x-3) Simplify

2 min read Jun 16, 2024
(x+2)(x-2)(x+3)(x-3) Simplify

Simplifying (x+2)(x-2)(x+3)(x-3)

This expression represents a multiplication of four binomial factors. To simplify it, we can utilize a pattern called the difference of squares.

Difference of Squares

The difference of squares pattern states:

(a + b)(a - b) = a² - b²

We can apply this pattern to our expression:

  • Step 1: Notice that (x + 2)(x - 2) and (x + 3)(x - 3) both follow the difference of squares pattern.

  • Step 2: Apply the pattern to each pair:

    • (x + 2)(x - 2) = x² - 2² = x² - 4
    • (x + 3)(x - 3) = x² - 3² = x² - 9

  • Step 3: Now our expression becomes: (x² - 4)(x² - 9)

  • Step 4: Again, we can apply the difference of squares pattern to this remaining multiplication:

    • (x² - 4)(x² - 9) = (x²)² - 4² = x⁴ - 16

Simplified Expression

Therefore, the simplified form of (x + 2)(x - 2)(x + 3)(x - 3) is x⁴ - 16.

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