Answer:
To multiply the given polynomials (x+6)(x+7), you can use the distributive property or the FOIL method (First, Outer, Inner, Last). Here's how you can do it using the FOIL method:
1. **First** - Multiply the first terms of each binomial: \(x \cdot x = x^2\).
2. **Outer** - Multiply the outer terms: \(x \cdot 7 = 7x\).
3. **Inner** - Multiply the inner terms: \(6 \cdot x = 6x\).
4. **Last** - Multiply the last terms of each binomial: \(6 \cdot 7 = 42\).
Now, add all these results together:
\[
x^2 + 7x + 6x + 42
\]
Combine like terms:
\[
x^2 + (7x + 6x) + 42
\]
\[
x^2 + 13x + 42
\]
So, the product of the given polynomials \((x+6)(x+7)\) is \(x^2 + 13x + 42\).
Explanation: