Math Snap

STEP 1

1. We are given an expression $(2x^2 - y)^2$ that needs to be expanded.
2. The expansion will involve using the binomial theorem or the distributive property.
3. The final result should be expressed as a polynomial in standard form.

STEP 2

1. Apply the binomial expansion formula to $(2x^2 - y)^2$.
2. Simplify the resulting expression.
3. Write the polynomial in standard form.

STEP 3

Apply the binomial expansion formula $(a - b)^2 = a^2 - 2ab + b^2$ to the expression $(2x^2 - y)^2$.
Let $a = 2x^2$ and $b = y$.
$$(2x^2 - y)^2 = (2x^2)^2 - 2(2x^2)(y) + y^2$$

STEP 4

Calculate each term in the expansion:
1. Calculate $(2x^2)^2$:
$$(2x^2)^2 = 4x^4$$ 2. Calculate $-2(2x^2)(y)$:
$$-2(2x^2)(y) = -4x^2y$$ 3. Calculate $y^2$:
$$y^2 = y^2$$

STEP 5

Combine all the terms from the expansion:
$$4x^4 - 4x^2y + y^2$$

Write the polynomial in standard form, which is already achieved:
$$4x^4 - 4x^2y + y^2$$ The expanded polynomial in standard form is:
$$\boxed{4x^4 - 4x^2y + y^2}$$