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$\frac{625 \times 625 - 225 \times 225}{625 - 225} = ?$

400
850
1525
1000

Answer :

To solve the expression [tex]\frac{625 \times 625 - 225 \times 225}{625 - 225}[/tex], let's start by understanding the components of the expression.

Step-by-step Solution

  1. Identify the Structure: The expression can be recognized as a form of the difference of squares. The difference of squares formula states that [tex]a^2 - b^2 = (a - b)(a + b)[/tex]. In this question, the numerator is a difference of squares.

  2. Rewrite the Numerator:

    • Let [tex]a = 625[/tex] and [tex]b = 225[/tex].
    • According to the formula, [tex]a^2 - b^2 = (a - b)(a + b)[/tex].
    • Therefore, $625^2 - 225^2[tex]can be factored as[/tex](625 - 225)(625 + 225)$.

  3. Substitute Back:

    • Substituting these values into the expression, we have:

    [tex]\frac{(625 - 225)(625 + 225)}{625 - 225}[/tex]

  4. Simplify:

    • Notice that [tex](625 - 225)[/tex] is common in both the numerator and the denominator. By the property of division, [tex]\frac{(625 - 225)(625 + 225)}{625 - 225}[/tex] simplifies to $625 + 225$.

  5. Calculate:

    • Adding 625 and 225 gives:

    [tex]625 + 225 = 850.[/tex]

Thus, the result of the expression is $850$.

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Rewritten by : Jeany

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