Factor. 9t^2 - 30t + 25 ______

Identify Form: Identify the form of the quadratic trinomial. The given expression 9t^2 - 30t + 25 is a quadratic trinomial which can potentially be factored into the form (at - b)^2, where a and b are constants.Rewrite 9t^2: Rewrite 9t^2 as the square of a binomial. 9t^2 can be expressed as (3t)^2 because 3^2 equals 9.Rewrite 25: Rewrite 25 as the square of a binomial. 25 can be expressed as 5^2 because 5^2 equals 25.Identify a and b: Identify the values of a and b. From the previous steps, we have identified that a = 3t and b = 5.Check Middle Term: Check if the middle term -30t fits the pattern 2ab. For the expression to be a perfect square trinomial, the middle term should be -2ab. Let's check if -30t equals -2 * 3t * 5. -2 * 3t * 5 = -30t, which matches the middle term of the given expression.Write Factored Form: Write the factored form of the expression 9t^2 - 30t + 25. Since the expression fits the pattern of a perfect square trinomial a^2 - 2ab + b^2, it can be factored as (a - b)^2. Therefore, the factored form is (3t - 5)^2.

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Factor. $\newline$ $9t^2 - 30t + 25$

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Q. Factor.

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9t^2 - 30t + 25

Identify Form: Identify the form of the quadratic trinomial. $\newline$ The given expression $9t^2 - 30t + 25$ is a quadratic trinomial which can potentially be factored into the form $(at - b)^2$ , where $a$ and $b$ are constants.
Rewrite $9t^2$ : Rewrite $9t^2$ as the square of a binomial. $\newline$ $9t^2$ can be expressed as $(3t)^2$ because $3^2$ equals $9$ .
Rewrite $25$ : Rewrite $25$ as the square of a binomial. $\newline$ $25$ can be expressed as $5^2$ because $5^2$ equals $25$ .
Identify $a$ and $b$ : Identify the values of $a$ and $b$ . From the previous steps, we have identified that $a = 3t$ and $b = 5$ .
Check Middle Term: Check if the middle term $-30t$ fits the pattern $2ab$ . For the expression to be a perfect square trinomial, the middle term should be $-2ab$ . Let's check if $-30t$ equals $-2 \times 3t \times 5$ . $-2 \times 3t \times 5 = -30t$ , which matches the middle term of the given expression.
Write Factored Form: Write the factored form of the expression $9t^2 - 30t + 25$ . Since the expression fits the pattern of a perfect square trinomial $a^2 - 2ab + b^2$ , it can be factored as $(a - b)^2$ . Therefore, the factored form is $(3t - 5)^2$ .