Factor. 4r^2 + 20r + 25 ______

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Identify Form: Identify the form of the quadratic trinomial. The given expression 4r^2 + 20r + 25 is a quadratic trinomial in the form of ar^2 + br + c.Find Common Factor: Look for a common factor in all three terms. In this case, there is no common factor other than 1, so we proceed to factor by grouping or by using the perfect square trinomial formula.Recognize Pattern: Recognize the pattern of a perfect square trinomial. A perfect square trinomial is in the form a^2 + 2ab + b^2, which can be factored into (a + b)^2. We need to check if 4r^2 + 20r + 25 fits this pattern.Rewrite 4r^2: Rewrite 4r^2 in the form of a^2. 4r^2 can be written as (2r)^2, which suggests that a = 2r.Rewrite 25: Rewrite 25 in the form of b^2. 25 can be written as 5^2, which suggests that b = 5.Check Middle Term: Check if the middle term fits the pattern 2ab. For the expression to be a perfect square trinomial, the middle term should be 2 * a * b. Let's check: 2 * (2r) * 5 = 20r, which matches the middle term of the given expression.Write Factored Form: Write the factored form of the expression 4r^2 + 20r + 25. Since we have confirmed that the expression is a perfect square trinomial, we can write it as (a + b)^2. Therefore, the factored form is (2r + 5)^2.

Factor. $\newline$ $4r^2 + 20r + 25$

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Factor.\newline4r2+20r+254r^2 + 20r + 254r2+20r+25

Factor. $\newline$ $4r^2 + 20r + 25$