By using the formula [tex](a^{2} -b^{2})=(a+b)(a-b)[/tex] the factors of [tex]36x^{8}-49[/tex] are [tex](6x^{4}+7)(\sqrt{6}x^{2} +\sqrt{7})(\sqrt{6}x^{2} -7)[/tex].
Factorization or factoring consists of writing a number or another object as a product of several factors. To solve a quadratic equation we required to make factors by factorization. It makes easier in finding values of variables.
The given expression is [tex]36x^{8}-49[/tex] and we need to find the factors using the formula [tex]a^{2} -b^{2} =(a+ b )(a-b)[/tex] .
[tex]36x^{8}-49=(6x^{4}) ^{2} -7^{2}[/tex] ([tex]A^{2} -B^{2} =(A+B)(A-B)[/tex])
We have broken power of x in 2 and 4 which together combines 2*4=8.
=[tex](6x^{4}+7)(6x^{4}-7)[/tex]
=[tex](6x^{4}+7){(\sqrt{6}x^{2}) ^{2}-\sqrt{7} ^{2}[/tex]
=[tex](6x^{4}+7)[(\sqrt{6} x^{2} +7)(\sqrt{6}x^{2} -\sqrt{7}) ][/tex]
Hence factors of [tex]36x^{8}-49[/tex] are [tex](6x^{4} +7)[/tex], [tex](\sqrt{6}x^{4}+\sqrt{7})[/tex],[tex](\sqrt{6}x^{2} -\sqrt{7} )[/tex].
Learn more about factorization at https://brainly.com/question/25829061
#SPJ2
