Factoring Difference of Squares Math Example 1

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Example 1

easy
Factor x2−49x^2 - 49.

Solution

  1. 1
    Step 1: Recognize the form a2−b2a^2 - b^2 where a=xa = x and b=7b = 7.
  2. 2
    Step 2: Apply the formula: (a+b)(a−b)=(x+7)(x−7)(a+b)(a-b) = (x+7)(x-7).
  3. 3
    Step 3: Verify: (x+7)(x−7)=x2−7x+7x−49=x2−49(x+7)(x-7) = x^2 - 7x + 7x - 49 = x^2 - 49 ✓

Answer

(x+7)(x−7)(x + 7)(x - 7)
The difference of squares pattern a2−b2=(a+b)(a−b)a^2 - b^2 = (a+b)(a-b) works because the middle terms cancel. Both terms must be perfect squares separated by subtraction.

About Factoring Difference of Squares

Recognizing and factoring expressions of the form a2−b2a^2 - b^2 into the product (a+b)(a−b)(a + b)(a - b).

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More Factoring Difference of Squares Examples

Example 2 medium

Factor [formula].

Example 3 easy

Factor [formula].

Example 4 hard

Factor [formula] completely.

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