Factor. 4m^2 - 20m + 25 ______

Check Perfect Square Trinomial: 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 or (a + b)^2 = a^2 + 2ab + b^2. We need to check if 4m^2 - 20m + 25 fits this pattern.Identify Square Roots: Identify the square root of the first term and the last term. The square root of 4m^2 is 2m, and the square root of 25 is 5. We will check if the middle term is twice the product of these two numbers.Verify Middle Term: Check if the middle term is twice the product of the square roots from Step 2. 2 * (2m) * 5 = 20m, which matches the middle term of the quadratic expression. This confirms that the expression is a perfect square trinomial.Write Factored Form: Write the factored form using the square roots from Step 2. Since the middle term is negative, we use the pattern (a - b)^2 to write the factored form. Therefore, the factored form of 4m^2 - 20m + 25 is (2m - 5)^2.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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4m^2 - 20m + 25

Check Perfect Square Trinomial: Determine if the quadratic can be factored as a perfect square trinomial. A perfect square trinomial is in the form $(a - b)^2 = a^2 - 2ab + b^2$ or $(a + b)^2 = a^2 + 2ab + b^2$ . We need to check if $4m^2 - 20m + 25$ fits this pattern.
Identify Square Roots: Identify the square root of the first term and the last term. $\newline$ The square root of $4m^2$ is $2m$ , and the square root of $25$ is $5$ . We will check if the middle term is twice the product of these two numbers.
Verify Middle Term: Check if the middle term is twice the product of the square roots from Step $2$ . $\newline$ $2 \times (2m) \times 5 = 20m$ , which matches the middle term of the quadratic expression. This confirms that the expression is a perfect square trinomial.
Write Factored Form: Write the factored form using the square roots from Step $2$ . $\newline$ Since the middle term is negative, we use the pattern $(a - b)^2$ to write the factored form. Therefore, the factored form of $4m^2 - 20m + 25$ is $(2m - 5)^2$ .