Answer :
Sure! To factor the polynomial expression [tex]\( 9x^4 - 4 \)[/tex], we can use the difference of squares method. Here’s a step-by-step explanation:
1. Recognize that the expression is a difference of squares. The expression is:
[tex]\[
9x^4 - 4
\][/tex]
It can be written as:
[tex]\[
(3x^2)^2 - 2^2
\][/tex]
2. Use the formula for the difference of squares, which is:
[tex]\[
a^2 - b^2 = (a - b)(a + b)
\][/tex]
In this case, identify:
[tex]\[
a = 3x^2 \quad \text{and} \quad b = 2
\][/tex]
3. Substitute these values into the formula:
[tex]\[
(3x^2)^2 - 2^2 = (3x^2 - 2)(3x^2 + 2)
\][/tex]
So, the factored form of the polynomial [tex]\( 9x^4 - 4 \)[/tex] is:
[tex]\[
(3x^2 - 2)(3x^2 + 2)
\][/tex]
This is the complete factorization using the difference of squares.
1. Recognize that the expression is a difference of squares. The expression is:
[tex]\[
9x^4 - 4
\][/tex]
It can be written as:
[tex]\[
(3x^2)^2 - 2^2
\][/tex]
2. Use the formula for the difference of squares, which is:
[tex]\[
a^2 - b^2 = (a - b)(a + b)
\][/tex]
In this case, identify:
[tex]\[
a = 3x^2 \quad \text{and} \quad b = 2
\][/tex]
3. Substitute these values into the formula:
[tex]\[
(3x^2)^2 - 2^2 = (3x^2 - 2)(3x^2 + 2)
\][/tex]
So, the factored form of the polynomial [tex]\( 9x^4 - 4 \)[/tex] is:
[tex]\[
(3x^2 - 2)(3x^2 + 2)
\][/tex]
This is the complete factorization using the difference of squares.
