Given the expression:
[tex]7a^{10}-112a^2[/tex]We know that 7*16 = 112 and a²*a⁸=a¹⁰, then:
[tex]7a^{10}-112a^2=7a^2(a^8-16)[/tex]Additionally, applying the difference of squares:
[tex]a^8-16=(a^4+4)(a^4-4)[/tex]Using the same identity:
[tex]a^4-4=(a^2-2)(a^2+2)[/tex]For the first term of the lat result:
[tex]a^2-2=(a+\sqrt{2})(a-\sqrt{2})[/tex]Putting them together:
[tex]7a^{10}-112a^2=7a^2(a^4+4)(a^2+2)(a+\sqrt{2})(a-\sqrt{2})[/tex]
