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Answer :
To factor the expression [tex]\(25x^4 - 9\)[/tex], you can follow these steps:
1. Recognize the difference of squares pattern: The expression [tex]\(25x^4 - 9\)[/tex] can be rewritten as a difference of squares. Recall that a difference of squares takes the form [tex]\(a^2 - b^2 = (a - b)(a + b)\)[/tex].
2. Identify the squares:
- [tex]\(25x^4\)[/tex] is a perfect square because [tex]\((5x^2)^2 = 25x^4\)[/tex].
- [tex]\(9\)[/tex] is also a perfect square because [tex]\(3^2 = 9\)[/tex].
3. Apply the difference of squares formula:
Using the pattern [tex]\(a^2 - b^2 = (a - b)(a + b)\)[/tex], set [tex]\(a = 5x^2\)[/tex] and [tex]\(b = 3\)[/tex].
4. Write the factors:
- The expression [tex]\(25x^4 - 9\)[/tex] factors into [tex]\((5x^2 - 3)(5x^2 + 3)\)[/tex].
So, the factored form of the expression [tex]\(25x^4 - 9\)[/tex] is [tex]\((5x^2 - 3)(5x^2 + 3)\)[/tex].
1. Recognize the difference of squares pattern: The expression [tex]\(25x^4 - 9\)[/tex] can be rewritten as a difference of squares. Recall that a difference of squares takes the form [tex]\(a^2 - b^2 = (a - b)(a + b)\)[/tex].
2. Identify the squares:
- [tex]\(25x^4\)[/tex] is a perfect square because [tex]\((5x^2)^2 = 25x^4\)[/tex].
- [tex]\(9\)[/tex] is also a perfect square because [tex]\(3^2 = 9\)[/tex].
3. Apply the difference of squares formula:
Using the pattern [tex]\(a^2 - b^2 = (a - b)(a + b)\)[/tex], set [tex]\(a = 5x^2\)[/tex] and [tex]\(b = 3\)[/tex].
4. Write the factors:
- The expression [tex]\(25x^4 - 9\)[/tex] factors into [tex]\((5x^2 - 3)(5x^2 + 3)\)[/tex].
So, the factored form of the expression [tex]\(25x^4 - 9\)[/tex] is [tex]\((5x^2 - 3)(5x^2 + 3)\)[/tex].
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