Factor. m^2 + 10m + 25 ______

Check Pattern: Determine if the quadratic can be factored as a perfect square trinomial. A perfect square trinomial is in the form (a + b)^2 = a^2 + 2ab + b^2. We need to check if m^2 + 10m + 25 fits this pattern.Identify Terms: Identify the square root of the first term and the last term. The square root of m^2 is m, and the square root of 25 is 5. So, we have a = m and b = 5.Middle Term Check: Check if the middle term fits the pattern 2ab. For our expression, the middle term is 10m. We need to see if this equals 2 * m * 5. 2 * m * 5 = 10m, which matches the middle term of our expression.Write Factored Form: Write the factored form using the identified values of a and b. Since the expression fits the pattern of a perfect square trinomial, we can write it as (a + b)^2. Therefore, the factored form is (m + 5)^2.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

\newline

m^2 + 10m + 25

Check Pattern: Determine if the quadratic can be factored as a perfect square trinomial. $\newline$ A perfect square trinomial is in the form $(a + b)^2 = a^2 + 2ab + b^2$ . We need to check if $m^2 + 10m + 25$ fits this pattern.
Identify Terms: Identify the square root of the first term and the last term. $\newline$ The square root of $m^2$ is $m$ , and the square root of $25$ is $5$ . So, we have $a = m$ and $b = 5$ .
Middle Term Check: Check if the middle term fits the pattern $2ab$ . For our expression, the middle term is $10m$ . We need to see if this equals $2 \times m \times 5$ . $2 \times m \times 5 = 10m$ , which matches the middle term of our expression.
Write Factored Form: Write the factored form using the identified values of $a$ and $b$ . Since the expression fits the pattern of a perfect square trinomial, we can write it as $(a + b)^2$ . Therefore, the factored form is $(m + 5)^2$ .