How do you factorise fully 3 a^3 b + 12 a^2 b^2 + 9 a^5 b^3?
To factorize 3a^3b + 12a^2b^2 + 9a^5b^3 fully, we need to first identify the common factor among the terms, which is 3a^2b. We can factor this out using the distributive property, as follows:
3a^3b + 12a^2b^2 + 9a^5b^3 = 3a^2b (a + 4b + 3a^3b^2)
Therefore, the fully factorized form of the expression is 3a^2b(a + 4b + 3a^3b^2).
To factorize an expression means to rewrite it as a product of simpler expressions or factors. It is a common algebraic technique used to simplify and solve equations.
The common factor in the expression is 3a^2b. This can be identified by finding the highest common factor of the terms.
To factorize the expression fully, you need to identify the common factor, which is 3a^2b, and factor it out using the distributive property. The resulting expression will be fully factorized.
Factorizing expressions is important because it simplifies them and makes them easier to work with. It can also help in solving equations and identifying patterns in mathematical expressions.
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