Question

determine if the expression shown can be factored using differences of two squares 25x^4-3x^2
Will It be
Difference of two squares cannot be used because there are more than two terms
The expression can be factored using differences of two squares
Differences of two squares cannot be used because all terms are not perfect
Differences of two squares cannot be used because two terms are being added together

Answer 1

To determine whether the expression \( 25x^4 - 3x^2 \) can be factored using the difference of two squares, we need to first recognize that the difference of squares can only be applied to expressions that are in the form \( a^2 - b^2 \).

1. **Identify terms:** The expression can be rewritten as \( 25x^4 - 3x^2 = (5x^2)^2 - ( \sqrt{3}x)^2 \).
2. **Form:** This expression is indeed in the form of \( a^2 - b^2 \) where \( a = 5x^2 \) and \( b = \sqrt{3}x \).

Using the difference of squares formula \( a^2 - b^2 = (a - b)(a + b) \), we can factor it as follows:

\[
(5x^2 - \sqrt{3}x)(5x^2 + \sqrt{3}x)
\]

Given this analysis, the correct conclusion is:

**The expression can be factored using differences of two squares.**