Factor the expression 4x^2-20xy+25y^2
into a product of binomials
(2x-5y)(2x-5y)
It can't get easier than this.
To factor the expression 4x^2 - 20xy + 25y^2, we need to look for a pattern that can help us write it as a product of binomials.
First, let's examine the expression and see if it fits the pattern of a perfect square trinomial. A perfect square trinomial is an expression of the form (a^2 + 2ab + b^2) or (a^2 - 2ab + b^2).
In our case, the expression 4x^2 - 20xy + 25y^2 doesn't fit the pattern of a perfect square trinomial.
Next, let's try factoring the expression by grouping. We'll group the terms in pairs and look for common factors.
Grouping the terms in pairs, we have:
(4x^2 - 20xy) + (25y^2)
Taking out the greatest common factor from each pair, we get:
4x(x - 5y) + 25y^2
Now, notice that we have a common factor of (x - 5y) in both terms. We can factor it out to obtain the final factored form:
(x - 5y)(4x + 25y)
Therefore, the expression 4x^2 - 20xy + 25y^2 can be factored as (x - 5y)(4x + 25y).