Factorize the following:
2a⁴b⁴ − 3a³b⁵ + 4a²b⁵

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Solution

The greatest common factor of the terms 2a⁴b⁴, -3a³b⁵ and 4a²b⁵ of the expression 2a⁴b⁴ - 3a³b⁵ + 4a²b⁵ is a²b⁴.

Now,
2a⁴b⁴= a²b⁴ $\times$ 2a²
-3a³b⁵= a²b⁴ $\times$ -3ab
4a²b⁵= a²b⁴ $\times$ 4b

Hence, (2a⁴b⁴ - 3a³b⁵ + 4a²b⁵) can be factorised as [a²b⁴(2a² - 3ab + 4b)].

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