➤ Answers
To factor these expressions, we need to understand the pattern in factoring the difference of two squares:
[tex]{\boxed{\tt{a^{2}-b^{2}=(a+b)(a-b)}}}[/tex]
1.
[tex]{\large{\boxed{\underline{\tt{(x^{2}+9)(x+3)(x-3)}}}}}[/tex]
Step by Step Explanation:
- [tex]{\tt{x^{4}-81}}[/tex]
We need to find the square roots of the two terms.
- [tex]{\tt{{\sqrt{{x}^{4}}}}={x}^{2}}[/tex]
- [tex]{\tt{{\sqrt{81}}}=9}[/tex]
Now we make sure that it appears as a product of the sum and difference of the two terms:
- [tex]{\tt{=(x^{2}+9)(x^{2}-9)}}[/tex]
We can see that there is difference of two squares among the factors. So we factor it completely using the pattern written above.
- [tex]{\tt{=(x^{2}+9)(x+3)(x-3)}}[/tex]
2.
[tex]{\large{\boxed{\underline{\tt{(7x+10)(7x-10)}}}}}[/tex]
Step by Step Explanation
- [tex]{\tt{49x^{2}-100}}[/tex]
We need to find the square roots of the two terms.
- [tex]{\tt{{\sqrt{49{x}^{2}}}}=7x^{2}}[/tex]
- [tex]{\tt{{\sqrt{100}}}=10}[/tex]
Now we make sure that it appears as a product of the sum and difference of the two terms:
- [tex]{\tt{=(7x+10)(7x-10)}}[/tex]
[tex]{\: \:}[/tex]
[tex]{\huge{\underline{\sf{Hope\:It\:Helps}}}}[/tex]
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