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Question 2

2.1 Factorize the following:

2.1.1

[tex]\[
8a^3 + 4a^2
\][/tex]

Sagot :

GinnyAnsweridn
Sure, let's factorize the given expression step by step.

Given the expression:
[tex]\[ 8a^3 + 4a^2 \][/tex]

Step 1: Identify common factors

First, we need to look for the greatest common factor (GCF) of the terms in the expression.

The terms are [tex]\( 8a^3 \)[/tex] and [tex]\( 4a^2 \)[/tex].

The coefficients 8 and 4 have a GCF of 4.

Both terms also have a common factor of [tex]\( a^2 \)[/tex].

So, the overall GCF is [tex]\( 4a^2 \)[/tex].

Step 2: Factor out the GCF

Now, we factor out [tex]\( 4a^2 \)[/tex] from each term:

[tex]\[ 8a^3 + 4a^2 = 4a^2 \cdot (2a) + 4a^2 \cdot (1) \][/tex]

Step 3: Simplify the factored expression

Combine the factored parts:

[tex]\[ 4a^2 (2a) + 4a^2 (1) = 4a^2 (2a + 1) \][/tex]

So, the factorized form of the expression [tex]\( 8a^3 + 4a^2 \)[/tex] is:

[tex]\[ 4a^2 (2a + 1) \][/tex]

That's the final factored expression.
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