Question

question
expand and state your answer as a polynomial in standard form.
$(2x^2 - y)^2$

Explanation:

Step1: Recall the perfect square formula

The perfect square formula is \((a - b)^2 = a^2 - 2ab + b^2\). Here, \(a = 2x^2\) and \(b = y\).

Step2: Substitute \(a\) and \(b\) into the formula

First, calculate \(a^2\): \((2x^2)^2 = 4x^4\).
Then, calculate \(2ab\): \(2\times(2x^2)\times y = 4x^2y\).
Next, calculate \(b^2\): \(y^2\).
Now, substitute these into the formula: \((2x^2 - y)^2=(2x^2)^2-2\times(2x^2)\times y + y^2\).

Step3: Simplify the expression

Simplify each term: \((2x^2)^2 = 4x^4\), \(2\times(2x^2)\times y = 4x^2y\), so the expression becomes \(4x^4 - 4x^2y + y^2\).

Answer:

\(4x^4 - 4x^2y + y^2\)