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

Check Quadratic Form: Determine if the quadratic can be factored as a perfect square trinomial. A perfect square trinomial is in the form (ay + b)^2 = a^2y^2 + 2aby + b^2. We can compare the given quadratic 4y^2 - 20y + 25 with the general form to see if it matches.Identify First Term: Identify the square of the first term. The first term is 4y^2, which is the square of (2y)^2.Identify Last Term: Identify the square of the last term. The last term is 25, which is the square of 5^2.Check Middle Term: Check if the middle term is twice the product of the bases of the first and last terms. The middle term is -20y, and twice the product of the bases from step 2 and step 3 is 2*(2y)*5 = 20y. Since the middle term is negative, we need to consider -20y, which matches the middle term.Write Factored Form: Write the factored form as a perfect square trinomial. Since all the terms match the perfect square trinomial form, we can write the factored form as (2y - 5)^2.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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4y^2 - 20y + 25

Check Quadratic Form: Determine if the quadratic can be factored as a perfect square trinomial. $\newline$ A perfect square trinomial is in the form $(ay + b)^2 = a^2y^2 + 2aby + b^2$ . $\newline$ We can compare the given quadratic $4y^2 - 20y + 25$ with the general form to see if it matches.
Identify First Term: Identify the square of the first term. $\newline$ The first term is $4y^2$ , which is the square of $(2y)^2$ .
Identify Last Term: Identify the square of the last term. $\newline$ The last term is $25$ , which is the square of $5^2$ .
Check Middle Term: Check if the middle term is twice the product of the bases of the first and last terms. $\newline$ The middle term is $-20y$ , and twice the product of the bases from step $2$ and step $3$ is $2\times(2y)\times5 = 20y$ . Since the middle term is negative, we need to consider $-20y$ , which matches the middle term.
Write Factored Form: Write the factored form as a perfect square trinomial. $\newline$ Since all the terms match the perfect square trinomial form, we can write the factored form as $(2y - 5)^2$ .