Here, we are having a quadratic equation in one variable because the highest degree is 2 and contains only one variable i.e. x
Given, equation:
[tex]81 {x}^{2} - 100[/tex]
Now, if we observe the terms used in the polynomial, 81x² and 100 separated by a negative sign, we can analyze and can factorise using the identity:
[tex] {a}^{2} - {b}^{2} = (a+ b)(a - b)[/tex]
Consider:
So, let's factorise by using the above identity
[tex]81 {x}^{2} - 100[/tex]
[tex](9x) {}^{2} - (10) {}^{2} [/tex]
Here, a = 9x and b = 10,
[tex](9x + 10)(9x - 10)[/tex]
Is the factorised form of 81x² - 100
So Correct Option is: Option C
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