use polynomial identities to factor the polynomials or simplify the expressions.

Question

x^9-8

8x^3+y^9

x^6-27y^3

4x^2+144

216+27y^12

64x^3-125y^6

Answer 1

A³ - B³ = (A - B)(A² + AB + B²) and A³ + B³ = (A + B)(A² - AB + B²)

So, for example, 8x³ + y⁹ = (2x)³ + (y³)³ = (2x + y³)(4x² - 2xy³ + y⁶)

All of the other problems except for 4x² + 144 can be factored using the above formulas.

4x² + 144 = 4(x² + 36)

Answer 2

4x² + 144 = (2x + 12i) × (2x - 12i)

where i = √(-1)

If you are limited to the real number system, the best you can do is to factor 4 out, as previously demonstrated.