Question

7a^10 - 112a^2Please factor it and show your work

Answer 1

Given the expression:

`7a^(10)-112a^2`

We know that 7*16 = 112 and a²*a⁸=a¹⁰, then:

`7a^(10)-112a^2=7a^2(a^8-16)`

Additionally, applying the difference of squares:

`a^8-16=(a^4+4)(a^4-4)`

Using the same identity:

`a^4-4=(a^2-2)(a^2+2)`

For the first term of the lat result:

`a^2-2=(a+√(2))(a-√(2))`

Putting them together:

`7a^(10)-112a^2=7a^2(a^4+4)(a^2+2)(a+√(2))(a-√(2))`