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Answer :
To factor the expression [tex]\(9x^4 - 16\)[/tex], you can recognize it as a difference of squares. A difference of squares follows the identity:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
In the expression [tex]\(9x^4 - 16\)[/tex], you can see that both terms are perfect squares:
1. [tex]\(9x^4\)[/tex] can be written as [tex]\((3x^2)^2\)[/tex].
2. [tex]\(16\)[/tex] can be written as [tex]\((4)^2\)[/tex].
Now that you have identified both squares, you can apply the difference of squares formula:
[tex]\[ 9x^4 - 16 = (3x^2)^2 - (4)^2 \][/tex]
Using the formula [tex]\(a^2 - b^2 = (a - b)(a + b)\)[/tex], let:
- [tex]\(a = 3x^2\)[/tex]
- [tex]\(b = 4\)[/tex]
Now substitute these into the formula:
[tex]\[ (3x^2)^2 - (4)^2 = (3x^2 - 4)(3x^2 + 4) \][/tex]
So, the factored form of the expression [tex]\(9x^4 - 16\)[/tex] is:
[tex]\[ (3x^2 - 4)(3x^2 + 4) \][/tex]
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
In the expression [tex]\(9x^4 - 16\)[/tex], you can see that both terms are perfect squares:
1. [tex]\(9x^4\)[/tex] can be written as [tex]\((3x^2)^2\)[/tex].
2. [tex]\(16\)[/tex] can be written as [tex]\((4)^2\)[/tex].
Now that you have identified both squares, you can apply the difference of squares formula:
[tex]\[ 9x^4 - 16 = (3x^2)^2 - (4)^2 \][/tex]
Using the formula [tex]\(a^2 - b^2 = (a - b)(a + b)\)[/tex], let:
- [tex]\(a = 3x^2\)[/tex]
- [tex]\(b = 4\)[/tex]
Now substitute these into the formula:
[tex]\[ (3x^2)^2 - (4)^2 = (3x^2 - 4)(3x^2 + 4) \][/tex]
So, the factored form of the expression [tex]\(9x^4 - 16\)[/tex] is:
[tex]\[ (3x^2 - 4)(3x^2 + 4) \][/tex]
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