Question

Multiply the polynomial expression
(1/2^2-3)(4y^3+5x^2)

Answer 1

To multiply the polynomial expression \((\frac{1}{2^2} - 3)(4y^3 + 5x^2)\), we first simplify the constant coefficient.

1. Calculate \(\frac{1}{2^2}\):
\[
\frac{1}{2^2} = \frac{1}{4}
\]
So, \(\frac{1}{2^2} - 3\) becomes:
\[
\frac{1}{4} - 3 = \frac{1}{4} - \frac{12}{4} = -\frac{11}{4}
\]

2. Now we have:
\[
-\frac{11}{4}(4y^3 + 5x^2)
\]

3. We distribute \(-\frac{11}{4}\):
- Multiply \(-\frac{11}{4}\) by \(4y^3\):
\[
-\frac{11}{4} \cdot 4y^3 = -11y^3
\]
- Multiply \(-\frac{11}{4}\) by \(5x^2\):
\[
-\frac{11}{4} \cdot 5x^2 = -\frac{55}{4}x^2
\]

4. Combine the results:
\[
-11y^3 - \frac{55}{4}x^2
\]

Thus, the final result is:
\[
-11y^3 - \frac{55}{4}x^2
\]