What is the anwer of X2 – 25 FACTOR
The Correct Answer and Explanation is:
To factor the expression x2−25x^2 – 25×2−25, we recognize that it is a difference of squares. The general formula for factoring a difference of squares is: a2−b2=(a+b)(a−b)a^2 – b^2 = (a + b)(a – b)a2−b2=(a+b)(a−b)
In your case, the expression is: x2−25x^2 – 25×2−25
Here, x2x^2×2 is a perfect square (x2=x2x^2 = x^2×2=x2) and 25 is also a perfect square (25=5225 = 5^225=52).
We can now apply the difference of squares formula, where: a=xandb=5a = x \quad \text{and} \quad b = 5a=xandb=5
Thus, the factored form of x2−25x^2 – 25×2−25 is: (x+5)(x−5)(x + 5)(x – 5)(x+5)(x−5)
Explanation:
The difference of squares formula works because of how squares behave mathematically. Any expression of the form a2−b2a^2 – b^2a2−b2 can be factored into the product of two binomials: (a+b)(a + b)(a+b) and (a−b)(a – b)(a−b).
In this specific case, x2−25x^2 – 25×2−25 can be rewritten as: x2−52x^2 – 5^2×2−52
This fits the difference of squares pattern, and so we factor it as: (x+5)(x−5)(x + 5)(x – 5)(x+5)(x−5)
This factorization gives us two factors, x+5x + 5x+5 and x−5x – 5x−5, which are the roots of the equation x2−25=0x^2 – 25 = 0x2−25=0. To check the factorization, you can expand (x+5)(x−5)(x + 5)(x – 5)(x+5)(x−5) back: (x+5)(x−5)=x2−5x+5x−25=x2−25(x + 5)(x – 5) = x^2 – 5x + 5x – 25 = x^2 – 25(x+5)(x−5)=x2−5x+5x−25=x2−25
So, the factorization is correct.
Conclusion:
The factored form of x2−25x^2 – 25×2−25 is: (x+5)(x−5)(x + 5)(x – 5)(x+5)(x−5)
This method is a standard approach for factoring quadratic expressions that are a difference of squares.
