Question
determine if the expression shown can be factored using differences of two squares 3x^2-4
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
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
Answers
GPT-4o mini
The expression \( 3x^2 - 4 \) can indeed be analyzed for factoring using the difference of squares formula.
The difference of squares states that \( a^2 - b^2 = (a - b)(a + b) \). To apply this to the expression \( 3x^2 - 4 \), we can rewrite it as follows:
1. Recognize that \( 3x^2 \) can be written as \( \sqrt{3}x \) squared, or \((\sqrt{3} x)^2\).
2. Recognize that \( 4 \) can be written as \( 2^2\).
Thus, we can express the original expression as:
\[
(\sqrt{3}x)^2 - (2)^2
\]
Now, we can apply the difference of squares formula:
\[
(\sqrt{3}x - 2)(\sqrt{3}x + 2)
\]
Therefore, the expression \( 3x^2 - 4 \) can indeed be factored using the difference of squares.
The correct conclusion from the options provided is:
**The expression can be factored using differences of two squares.**
The difference of squares states that \( a^2 - b^2 = (a - b)(a + b) \). To apply this to the expression \( 3x^2 - 4 \), we can rewrite it as follows:
1. Recognize that \( 3x^2 \) can be written as \( \sqrt{3}x \) squared, or \((\sqrt{3} x)^2\).
2. Recognize that \( 4 \) can be written as \( 2^2\).
Thus, we can express the original expression as:
\[
(\sqrt{3}x)^2 - (2)^2
\]
Now, we can apply the difference of squares formula:
\[
(\sqrt{3}x - 2)(\sqrt{3}x + 2)
\]
Therefore, the expression \( 3x^2 - 4 \) can indeed be factored using the difference of squares.
The correct conclusion from the options provided is:
**The expression can be factored using differences of two squares.**