Factor completely. 9m^(2)+30 mn+25n^(2)=

Identify Structure: Identify the structure of the quadratic expression. The given expression is in the form of a quadratic trinomial ax^2 + bx + c. In this case, a = 9, b = 30, and c = 25, with m and n being the variables.Pattern Recognition: Look for a pattern that resembles a perfect square trinomial. A perfect square trinomial is of the form (x + y)^2 = x^2 + 2xy + y^2. We can see that 9m^2 is a perfect square (3m)^2, 25n^2 is a perfect square (5n)^2, and the middle term 30mn is twice the product of 3m and 5n, which suggests that the given expression might be a perfect square trinomial.Factor as Square of Binomial: Factor the expression as the square of a binomial. Since the expression fits the pattern of a perfect square trinomial, we can write it as the square of a binomial: (3m + 5n)^2. This is because (3m)^2 = 9m^2, 2*(3m)*(5n) = 30mn, and (5n)^2 = 25n^2.

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Q. Factor completely.

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9 m^{2}+30 m n+25 n^{2}=

Identify Structure: Identify the structure of the quadratic expression. $\newline$ The given expression is in the form of a quadratic trinomial $ax^2 + bx + c$ . In this case, $a = 9$ , $b = 30$ , and $c = 25$ , with $m$ and $n$ being the variables.
Pattern Recognition: Look for a pattern that resembles a perfect square trinomial. $\newline$ A perfect square trinomial is of the form $(x + y)^2 = x^2 + 2xy + y^2$ . We can see that $9m^2$ is a perfect square $(3m)^2$ , $25n^2$ is a perfect square $(5n)^2$ , and the middle term $30mn$ is twice the product of $3m$ and $5n$ , which suggests that the given expression might be a perfect square trinomial.
Factor as Square of Binomial: Factor the expression as the square of a binomial. $\newline$ Since the expression fits the pattern of a perfect square trinomial, we can write it as the square of a binomial: $(3m + 5n)^2$ . This is because $(3m)^2 = 9m^2$ , $2\cdot(3m)\cdot(5n) = 30mn$ , and $(5n)^2 = 25n^2$ .