Final answer:
To factorise 2x⁶-8 fully, we factor out the common factor of 2, resulting in 2(x⁶-4), and then recognize x⁶-4 as a difference of squares, further factorizing it into 2(x³-2)(x³+2).
Step-by-step explanation:
To factorise the expression 2x⁶−8, we need to find common factors. Here, we see that 2 is a common factor of both terms, and we can rewrite the expression as 2(x⁶−4). The term x⁶−4 can be further factorized since it represents a difference of squares: x³² - 2². This gives us 2(x³−2)(x³+2).
In general, when factorising expressions, we should look for common factors, differences of squares, perfect square trinomials, and other patterns that can simplify the expression into a product of simpler polynomials.