Question

Ay^7 + y^7 - ay^3 - y^3​

Answer 1

$ay^7+y^7-ay^3-y^3=(a+1)y^7-y^3(a+1)=\\\\=(a+1)(y^7-y^3)=(a+1)\cdot y^3\, (y^4-1)=\\\\=y^3\cdot (a+1)(y^2-1)(y^2+1)=y^3\cdot (a+1)\cdot (y-1)\cdot (y+1)\cdot (y^2+1)$

Answer 2

The given expression is: Ay^7 + y^7 - ay^3 - y^3.

This expression contains two terms with y^7 and two terms with y^3. We can factor out common terms from each set of terms:

y^7 can be factored as y^3 * y^4. y^3 can be factored as y^3.

Now, let's factor out the common terms:

Ay^7 + y^7 - ay^3 - y^3

= (Ay^3 + y^3) * y^4 - (ay^3 + y^3)

Now, we can factor out y^3 from both groups:

= y^3 * (Ay^4 + 1) - y^3 * (a + 1)

Now, we have y^3 as a common factor:

= y^3 * (Ay^4 - a - 1)

So, the factored expression is: y^3 * (Ay^4 - a - 1).