Question

factor the expression completely.
\\25x^2 - 144\\

• \\((5x - 12)(5x - 12)\\)
• \\((5x - 72)(5x + 2)\\)
• \\((5x + 12)(5x - 12)\\)
• \\((5x + 12)(5x + 12)\\)

Explanation:

🆕 New Concept Discovered: Difference of Squares
Subtracting one perfect square from another

Step 1: Identify the pattern

The given expression is:

$$ 25x^2 - 144 $$

Both terms are perfect squares separated by a subtraction sign. This fits the difference of squares algebraic identity:

$$ a^2 - b^2 = (a + b)(a - b) $$

Step 2: Find the square roots

Determine the values of \( a \) and \( b \) by taking the square root of each term:

$$ a = \sqrt{25x^2} = 5x $$

$$ b = \sqrt{144} = 12 $$

Step 3: Apply the formula

Substitute \( a = 5x \) and \( b = 12 \) into the factored form \( (a + b)(a - b) \):

$$ (5x + 12)(5x - 12) $$

Answer:

\( (5x + 12)(5x - 12) \) (Option 3)