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Answer :
To solve the expression [tex]\frac{625 \times 625 - 225 \times 225}{625 - 225}[/tex], we can utilize a mathematical identity known as the difference of squares. The formula for the difference of squares is:
[tex]a^2 - b^2 = (a - b)(a + b)[/tex]
In this problem, we recognize that 625 and 225 can both be expressed as perfect squares:
- [tex]625 = 25^2[/tex]
- [tex]225 = 15^2[/tex]
So, the original expression becomes:
[tex]\frac{25^2 \times 25^2 - 15^2 \times 15^2}{25^2 - 15^2}[/tex]
Using the difference of squares identity, we can rewrite the numerator as:
[tex]25^4 - 15^4 = (25^2 - 15^2)(25^2 + 15^2)[/tex]
Notice that [tex](25^2 - 15^2)[/tex] in the numerator matches the denominator, which means they will cancel each other out:
[tex]\frac{(25^2 - 15^2)(25^2 + 15^2)}{25^2 - 15^2} = 25^2 + 15^2[/tex]
Now we need to calculate [tex]25^2 + 15^2[/tex]:
[tex]25^2 = 625[/tex]
[tex]15^2 = 225[/tex]
So, [tex]25^2 + 15^2 = 625 + 225 = 850[/tex]
Therefore, the value of the expression is 850.
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