Answer :

Certainly! To factor the expression [tex]\( 4x^2y^2 - 28x^3 + 56x^4 \)[/tex], follow these steps:

1. Look for Common Factors:
- First, identify the greatest common factor (GCF) in all the terms of the expression.
- The terms are: [tex]\( 4x^2y^2 \)[/tex], [tex]\( -28x^3 \)[/tex], and [tex]\( 56x^4 \)[/tex].
- Notice that each term has a factor of at least [tex]\( 4x^2 \)[/tex].

2. Factor out the GCF:
- Factor out [tex]\( 4x^2 \)[/tex] from each term of the expression:
- From [tex]\( 4x^2y^2 \)[/tex], factoring out [tex]\( 4x^2 \)[/tex] leaves [tex]\( y^2 \)[/tex].
- From [tex]\( -28x^3 \)[/tex], factoring out [tex]\( 4x^2 \)[/tex] leaves [tex]\( -7x \)[/tex].
- From [tex]\( 56x^4 \)[/tex], factoring out [tex]\( 4x^2 \)[/tex] leaves [tex]\( 14x^2 \)[/tex].

- So, when you factor out [tex]\( 4x^2 \)[/tex], the expression becomes:
[tex]\[
4x^2(y^2 - 7x + 14x^2)
\][/tex]

3. Result:
- The fully factored form of the expression [tex]\( 4x^2y^2 - 28x^3 + 56x^4 \)[/tex] is:
[tex]\[
4x^2(14x^2 - 7x + y^2)
\][/tex]

This step-by-step approach highlights the process of finding the greatest common factor and simplifying the expression by factoring it out.

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