Multiply the polynomial expression

Question

(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: \[ -11y^3 - \frac{55}{4}x^2 \]