Answer :
To factor the expression [tex]\(9x^4 - 16\)[/tex], we can recognize it as a difference of squares. A difference of squares takes the form [tex]\(a^2 - b^2\)[/tex] and factors into [tex]\((a-b)(a+b)\)[/tex].
Let's identify the components:
1. First, express each term as a square:
- The term [tex]\(9x^4\)[/tex] can be rewritten as [tex]\((3x^2)^2\)[/tex].
- The term [tex]\(16\)[/tex] is already a perfect square: [tex]\(16 = 4^2\)[/tex].
Now the expression [tex]\(9x^4 - 16\)[/tex] becomes [tex]\((3x^2)^2 - 4^2\)[/tex].
2. Apply the difference of squares formula:
- Using the formula [tex]\(a^2 - b^2 = (a - b)(a + b)\)[/tex], where [tex]\(a = 3x^2\)[/tex] and [tex]\(b = 4\)[/tex].
3. Substitute [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the formula to get:
[tex]\[
(3x^2 - 4)(3x^2 + 4)
\][/tex]
This is the factored form of the expression [tex]\(9x^4 - 16\)[/tex].
Let's identify the components:
1. First, express each term as a square:
- The term [tex]\(9x^4\)[/tex] can be rewritten as [tex]\((3x^2)^2\)[/tex].
- The term [tex]\(16\)[/tex] is already a perfect square: [tex]\(16 = 4^2\)[/tex].
Now the expression [tex]\(9x^4 - 16\)[/tex] becomes [tex]\((3x^2)^2 - 4^2\)[/tex].
2. Apply the difference of squares formula:
- Using the formula [tex]\(a^2 - b^2 = (a - b)(a + b)\)[/tex], where [tex]\(a = 3x^2\)[/tex] and [tex]\(b = 4\)[/tex].
3. Substitute [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the formula to get:
[tex]\[
(3x^2 - 4)(3x^2 + 4)
\][/tex]
This is the factored form of the expression [tex]\(9x^4 - 16\)[/tex].
