Final answer:
To factorize the expression a² + ab - 2b², we can use the factoring method. The factorization of the given expression is (a - 2b)(a + b).
Step-by-step explanation:
To factorize the expression a² + ab - 2b², we can look for two binomials whose product equals the given expression. The coefficient of a² is 1, so the binomials will have the form (a + ?)(a + ?).
The constant term is -2b², so the signs in the binomials will be opposite.
We need to find two numbers whose product is -2b² and whose sum is ab. Those numbers are -2b and b.
Therefore, the factorization is (a - 2b)(a + b).