Factoring Difference of Squares Math Example 2

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Example 2

medium
Factor 16x2−25y216x^2 - 25y^2.

Solution

  1. 1
    Step 1: Write as (4x)2−(5y)2(4x)^2 - (5y)^2.
  2. 2
    Step 2: Apply the formula: (4x+5y)(4x−5y)(4x + 5y)(4x - 5y).
  3. 3
    Step 3: Verify: (4x+5y)(4x−5y)=16x2−20xy+20xy−25y2=16x2−25y2(4x+5y)(4x-5y) = 16x^2 - 20xy + 20xy - 25y^2 = 16x^2 - 25y^2 ✓

Answer

(4x+5y)(4x−5y)(4x + 5y)(4x - 5y)
When coefficients or multiple variables are involved, rewrite each term as a perfect square first. Here 16x2=(4x)216x^2 = (4x)^2 and 25y2=(5y)225y^2 = (5y)^2.

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 1 easy

Factor [formula].

Example 3 easy

Factor [formula].

Example 4 hard

Factor [formula] completely.

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