Question
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Answer
The factored form of the expression
is
.
Solution
To factorize the expression:
Step 1: Expand the Expression
First, distribute the
in the term
:
So, the expression becomes:
Step 2: Rearrange the Terms
Rearrange the expression to group like terms:
Step 3: Factor by Grouping
Group the terms as follows:
Factor out the common factors from each group:
-
From the first group
, factor out : -
From the second group
, factor out :
So, the expression now looks like:
Step 4: Factor Out the Common Binomial
Both terms contain the binomial
:
Final Factored Form:
Answer:
After factoring, the expression is (6 a – b) multiplied by (b + 2 c). Thus,
(6a − b)(b + 2c)
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Mind Expander
To factorise the expression
, we start by rearranging the terms:
Now observe that
can be rearranged as
, allowing us to group the
terms. Factoring out
gives us
. Ultimately, we can regroup and recast it as it ultimately leads to a simpler expression. Therefore, the resulting factorised form is:
Factorisation can be a fascinating journey back in time! For centuries, mathematicians like Al-Khwarizmi worked to solve polynomials, laying the groundwork for modern algebra. The word “algebra” itself is derived from the title of his pivotal work, which was all about balancing equations. So, as you dive into factorisation, you’re echoing a rich legacy of curious minds who sought to understand the mathematical relationships hidden within numbers!
Looking at real-world applications of factorisation, this technique isn’t just confined to classrooms. Engineers use it in designing structures and optimizing materials, while economists employ it to analyze data trends. Even computer scientists utilize it in algorithm development! Factorisation helps simplify complex calculations, ultimately making it a handy tool in various professions, showcasing its versatility beyond mere textbook exercises.