Answer :

To factor the expression [tex]\( 25x^4 - 60x^2y^2 + 36y^4 \)[/tex], we can follow the completing the square method with a focus on recognizing a perfect square trinomial. Here's how it's done:

1. Identify the Structure:
Notice that the expression is in the form of a quadratic in terms of [tex]\( x^2 \)[/tex]. Rewrite it as [tex]\( (5x^2)^2 - 2 \times 5x^2 \times 6y^2 + (6y^2)^2 \)[/tex].

2. Recognize as a Perfect Square Trinomial:
This expression matches the form of a perfect square trinomial, which is [tex]\( (a^2 - 2ab + b^2) \)[/tex] that factors into [tex]\( (a-b)^2 \)[/tex].

3. Apply the Pattern:
Here, [tex]\( a = 5x^2 \)[/tex] and [tex]\( b = 6y^2 \)[/tex]. Applying the perfect square trinomial formula, the expression can be rewritten as:

[tex]\[
(5x^2 - 6y^2)^2
\][/tex]

That's the factored form of the given expression, showing that it is a perfect square trinomial.

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Rewritten by : Barada