Question

simplify the polynomial expression: (4xy - 3)(8x^2 + 5y)

the simplified polynomial written in standard form is

Answer 1

To simplify the polynomial expression \( (4xy - 3)(8x^2 + 5y) \), we will use the distributive property (also known as the FOIL method for binomials).

1. **Distribute \( 4xy \) to both terms in the second polynomial:**
\[
4xy \cdot 8x^2 = 32x^3y
\]
\[
4xy \cdot 5y = 20xy^2
\]

2. **Distribute \(-3\) to both terms in the second polynomial:**
\[
-3 \cdot 8x^2 = -24x^2
\]
\[
-3 \cdot 5y = -15y
\]

3. **Combine all the results:**
\[
32x^3y + 20xy^2 - 24x^2 - 15y
\]

4. **Rearrange into standard form (typically writing terms in descending order of degree):**
\[
32x^3y + 20xy^2 - 24x^2 - 15y
\]

So, the simplified polynomial written in standard form is:
\[
32x^3y + 20xy^2 - 24x^2 - 15y
\]