Question

What is the foil method of (4-5x)(3x^2+4)

Answer 1

The FOIL method is a technique used to multiply two binomials. However, in this case, we are multiplying a binomial \( (4 - 5x) \) by a trinomial \( (3x^2 + 4) \). We will distribute each term in the binomial across each term in the trinomial.

1. **Distribute \( 4 \) to each term in \( (3x^2 + 4) \)**:
\[
4 \cdot 3x^2 + 4 \cdot 4 = 12x^2 + 16
\]

2. **Distribute \( -5x \) to each term in \( (3x^2 + 4) \)**:
\[
-5x \cdot 3x^2 + (-5x) \cdot 4 = -15x^3 - 20x
\]

3. **Combine the results**:
Now we add the two results together:
\[
12x^2 + 16 - 15x^3 - 20x
\]
Rearranging in standard form gives:
\[
-15x^3 + 12x^2 - 20x + 16
\]

Thus, the result of the multiplication \( (4 - 5x)(3x^2 + 4) \) is:
\[
-15x^3 + 12x^2 - 20x + 16
\]