How to Factorize the Expression 4m² - 49 for an 11-Year-Old

Let's learn how to factorize the expression 4m² - 49. Factorizing means breaking down an expression into simpler parts (called factors) that multiply together to give the original expression.

Step 1: Recognize the form

The expression looks like: a² - b², which is known as the difference of squares. Here, 4m² is a perfect square, and 49 is also a perfect square.

• 4m² = (2m)² because 2m × 2m = 4m²
• 49 = 7² because 7 × 7 = 49

Step 2: Use the difference of squares formula

The difference of squares formula is:

a² - b² = (a - b)(a + b)

So, for our expression, let a = 2m and b = 7.

Step 3: Write the factors

Using the formula:

4m² - 49 = (2m - 7)(2m + 7)

Step 4: Check your answer

If you multiply the two factors back, you get:

(2m - 7)(2m + 7) = (2m)(2m) + (2m)(7) - 7(2m) - 7(7) = 4m² + 14m - 14m - 49 = 4m² - 49

The middle terms +14m and -14m cancel out, so the multiplication returns to the original expression.

Summary:

4m² - 49 = (2m - 7)(2m + 7). This is the factorized form using the difference of squares method!