Answer:
[tex]\mathrm{1.\: \left(a+1\right)\left(a-1\right)\left(a^2+1+a\right)\left(a^2+1-a\right)}[/tex][tex]\mathrm{2.\: \left(2a^2+5\right)\left(2a^2-5\right)}[/tex]3. not factorable
4. (a + 9)(a - 9)
5. (2a² + 7)(2a² - 7)
6. 5 (2a + 3b)
7. 6a (a - 3)
8. 6a (4b - c)
9. 4 (x + 2)
10. 3 (x + y)
Step-by-step explanation:
[tex]\mathrm{1.\: a^6 - 1}\\\\\mathrm{=\left(a^2\right)^3-1^3}\\\\\mathrm{=\left(a^2-1\right)\left(a^4+a^2+1\right)}\\\\\mathrm{=\left(a+1\right)\left(a-1\right)\left(a^4+a^2+1\right)}\\\\\mathrm{=\left(a+1\right)\left(a-1\right)\left(a^2+1+a\right)\left(a^2+1-a\right)}[/tex]
[tex]\mathrm{2.\: 4a^4 - 25}\\\\\mathrm{=\left(2a^2\right)^2-5^2}\\\\\mathrm{=\left(2a^2+5\right)\left(2a^2-5\right)}[/tex]
4. a² - 81
= a² - 9²
= (a + 9)(a - 9)
5. 4a⁴ - 49
= (2a²)² - 7²
= (2a² + 7)(2a² - 7)