Question
Mutiply (2x-y)^2
Answers
GPT-4o mini
To multiply \((2x - y)^2\), you can use the formula for the square of a binomial, which states that \((a - b)^2 = a^2 - 2ab + b^2\).
Here, \(a = 2x\) and \(b = y\).
So, applying the formula:
\[
(2x - y)^2 = (2x)^2 - 2(2x)(y) + y^2
\]
Calculating each term:
1. \((2x)^2 = 4x^2\)
2. \(-2(2x)(y) = -4xy\)
3. \(y^2 = y^2\)
Putting it all together, we get:
\[
(2x - y)^2 = 4x^2 - 4xy + y^2
\]
Therefore, the expanded form of \((2x - y)^2\) is
\[
\boxed{4x^2 - 4xy + y^2}
\]
Here, \(a = 2x\) and \(b = y\).
So, applying the formula:
\[
(2x - y)^2 = (2x)^2 - 2(2x)(y) + y^2
\]
Calculating each term:
1. \((2x)^2 = 4x^2\)
2. \(-2(2x)(y) = -4xy\)
3. \(y^2 = y^2\)
Putting it all together, we get:
\[
(2x - y)^2 = 4x^2 - 4xy + y^2
\]
Therefore, the expanded form of \((2x - y)^2\) is
\[
\boxed{4x^2 - 4xy + y^2}
\]