[tex]x^{10} +y^4[/tex] cannot be factorized that is cannot be represented as products of lower degree polynomials.
Solution:
Need to factor [tex]x^{10} +y^4[/tex] using the sum of squares that is we need to factorize [tex]x^{10} +y^4[/tex]
[tex]x^{10}+y^{4}=x^{(5 \times 2)}+y^{(2 \times 2)}[/tex]
Using law of exponent [tex]\mathrm{a}^{(\mathrm{m} \times \mathrm{n})}=\left(\mathrm{a}^{\mathrm{m}}\right)^{\mathrm{n}}[/tex]
On applying this we get,
[tex]x^{10}+y^{4}=\left(x^{5}\right)^{2}+\left(y^{2}\right)^{2}[/tex]
But there is no direct formula of [tex]\mathrm{a}^{2}+\mathrm{b}^{2}[/tex] which can provide factors.
Hence we can say that [tex]x^{10} +y^4[/tex] cannot be factorize that is cannot be represented as products of lower degree polynomials.
