Question

do you use the foil method for (2x+3)(4x+5)

Answer 1

Yes, the FOIL method is a useful way to multiply two binomials like \((2x + 3)(4x + 5)\). FOIL stands for First, Outside, Inside, and Last, representing the pairs of terms that you multiply together.

Here's how you apply the FOIL method to the expression \((2x + 3)(4x + 5)\):

1. **First**: Multiply the first terms in each binomial.
\[
2x \cdot 4x = 8x^2
\]

2. **Outside**: Multiply the outer terms.
\[
2x \cdot 5 = 10x
\]

3. **Inside**: Multiply the inner terms.
\[
3 \cdot 4x = 12x
\]

4. **Last**: Multiply the last terms in each binomial.
\[
3 \cdot 5 = 15
\]

Now, add all these results together:
\[
8x^2 + 10x + 12x + 15
\]

Combine like terms (the \(10x\) and \(12x\)):
\[
8x^2 + 22x + 15
\]

So, the product of \((2x + 3)(4x + 5)\) is:
\[
\boxed{8x^2 + 22x + 15}
\]