Answer:
7a^2(a^4 + 4)(a^4 - 4)
Explanation:
To simplify 7a^10 - 112a^2, we need to find the greatest common factor (GCF) of the two terms and factor it out.
The GCF of 7a^10 and 112a^2 is 7a^2.
So, we can factor out 7a^2 from both terms, which gives:
7a^2(a^8 - 16)
Now, we can further simplify the expression by noticing that a^8 - 16 is a difference of squares. We can write it as:
a^8 - 16 = (a^4)^2 - 4^2 = (a^4 + 4)(a^4 - 4)
Therefore, the fully simplified expression is:
7a^2(a^4 + 4)(a^4 - 4)