I am doing the Factorization of simple algebraic expressions,


the question is telling me to factorise 2a^2b-8b^2c-4abc+4ab^2

To factorize the expression \( 2a^2b - 8b^2c - 4abc + 4ab^2 \), let's proceed step by step:

### Expression:
\[
2a^2b - 8b^2c - 4abc + 4ab^2
\]

### Step 1: Group terms that have common factors.
We will group the terms as follows:
\[
(2a^2b - 4abc) + (-8b^2c + 4ab^2)
\]

### Step 2: Factor out the common factors in each group.
For the first group \( (2a^2b - 4abc) \), the common factor is \( 2ab \):
\[
2ab(a - 2c)
\]
For the second group \( (-8b^2c + 4ab^2) \), the common factor is \( 4b^2 \):
\[
4b^2(-2c + a)
\]
which simplifies to:
\[
4b^2(a - 2c)
\]

### Step 3: Factor out the common binomial factor.
Now, we can factor out the common binomial factor \( (a - 2c) \):
\[
(2ab + 4b^2)(a - 2c)
\]

### Step 4: Simplify the remaining factor.
Notice that \( 2ab + 4b^2 \) has a common factor of \( 2b \), so we factor it out:
\[
2b(a + 2b)(a - 2c)
\]

### Final Factorized Form:
The fully factorized expression is:
\[
2b(a + 2b)(a - 2c)
\]

Would you like more details on any of these steps or have any questions?

Here are some related practice problems:
1. Factorize \( 3x^2y - 6xy^2 + 9xyz \).
2. Factorize \( 4m^2n - 8mn^2 + 12mn \).
3. Factorize \( 6pq - 9pr + 12qr \).
4. Factorize \( 5x^2y - 10xy + 15xy^2 \).
5. Factorize \( 7a^2b - 14ab^2 + 21abc \).

**Tip**: Always look for the greatest common factor (GCF) when factorizing algebraic expressions to simplify the process.

I am doing the Factorization of simple algebraic expressions, the question is telling me to factorise 2a^2b - 8b^2c - 4abc + 4ab^2.

Learn how to factorize the algebraic expression 2a^2b - 8b^2c - 4abc + 4ab^2 with a step-by-step solution. This problem covers key algebraic concepts such as factoring by grouping and using the greatest common factor. Suitable for students in Grades 8-10.

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