Question
Use the foil method to find the product
(4-5x)(3x^2+4)
(4-5x)(3x^2+4)
Answers
GPT-4o mini
To find the product of the expression \((4 - 5x)(3x^2 + 4)\) using the FOIL method, we recognize that FOIL is specifically for multiplying two binomials. However, we can expand this expression by distributing each term in the first binomial (4 and -5x) to each term in the second binomial (3x² and 4).
Let's start:
1. **Distribute \(4\)**:
- \(4 \cdot 3x^2 = 12x^2\)
- \(4 \cdot 4 = 16\)
2. **Distribute \(-5x\)**:
- \(-5x \cdot 3x^2 = -15x^3\)
- \(-5x \cdot 4 = -20x\)
Now combine all these results:
\[
12x^2 + 16 - 15x^3 - 20x
\]
Finally, let's rearrange this in standard polynomial form:
\[
-15x^3 + 12x^2 - 20x + 16
\]
So, the product of \((4 - 5x)(3x^2 + 4)\) is:
\[
-15x^3 + 12x^2 - 20x + 16
\]
Let's start:
1. **Distribute \(4\)**:
- \(4 \cdot 3x^2 = 12x^2\)
- \(4 \cdot 4 = 16\)
2. **Distribute \(-5x\)**:
- \(-5x \cdot 3x^2 = -15x^3\)
- \(-5x \cdot 4 = -20x\)
Now combine all these results:
\[
12x^2 + 16 - 15x^3 - 20x
\]
Finally, let's rearrange this in standard polynomial form:
\[
-15x^3 + 12x^2 - 20x + 16
\]
So, the product of \((4 - 5x)(3x^2 + 4)\) is:
\[
-15x^3 + 12x^2 - 20x + 16
\]