Question

Expand and state your answer as a polynomial in standard form.

left parenthesis, 4, x, to the power 5 , minus, y, right parenthesis, squared
(4x
5
−y)
2

Answer 1

To expand the expression \((4x^5 - y)^2\), we can use the formula for the square of a binomial, which is \((a - b)^2 = a^2 - 2ab + b^2\).

In this case:
- \(a = 4x^5\)
- \(b = y\)

Now, applying the formula:

1. **Calculate \(a^2\)**:
\[
(4x^5)^2 = 16x^{10}
\]

2. **Calculate \(-2ab\)**:
\[
-2(4x^5)(y) = -8x^5y
\]

3. **Calculate \(b^2\)**:
\[
y^2 = y^2
\]

Now, combine all these results together:

\[
(4x^5 - y)^2 = a^2 - 2ab + b^2 = 16x^{10} - 8x^5y + y^2
\]

Thus, the expanded form of \((4x^5 - y)^2\) in standard form is:

\[
\boxed{16x^{10} - 8x^5y + y^2}
\]