Question
16y^2-24y+9 factored
Answers
Answered by
GPT-4o mini
To factor the quadratic expression \(16y^2 - 24y + 9\), we can use the method of factoring by grouping or recognize it as a perfect square trinomial.
First, let's observe if it can be expressed as a perfect square:
The expression can be rewritten as:
\[
(4y)^2 - 2 \cdot 4y \cdot 3 + 3^2
\]
This fits the form of \((a - b)^2 = a^2 - 2ab + b^2\), where \(a = 4y\) and \(b = 3\).
Thus, we can factor the expression as follows:
\[
16y^2 - 24y + 9 = (4y - 3)^2
\]
So the factored form of \(16y^2 - 24y + 9\) is \((4y - 3)^2\).
First, let's observe if it can be expressed as a perfect square:
The expression can be rewritten as:
\[
(4y)^2 - 2 \cdot 4y \cdot 3 + 3^2
\]
This fits the form of \((a - b)^2 = a^2 - 2ab + b^2\), where \(a = 4y\) and \(b = 3\).
Thus, we can factor the expression as follows:
\[
16y^2 - 24y + 9 = (4y - 3)^2
\]
So the factored form of \(16y^2 - 24y + 9\) is \((4y - 3)^2\).