Question

Simplify the product using the distributive property.
​(xminus−22​)(xplus+77​)

Answer 1

To simplify the expression \((x - 22)(x + 77)\) using the distributive property (also known as the FOIL method for binomials), follow these steps:

1. **First**: Multiply the first terms.
\[
x \cdot x = x^2
\]

2. **Outer**: Multiply the outer terms.
\[
x \cdot 77 = 77x
\]

3. **Inner**: Multiply the inner terms.
\[
-22 \cdot x = -22x
\]

4. **Last**: Multiply the last terms.
\[
-22 \cdot 77 = -1694
\]

Putting it all together, we have:
\[
x^2 + 77x - 22x - 1694
\]

Now, combine the like terms (\(77x\) and \(-22x\)):
\[
x^2 + (77x - 22x) - 1694 = x^2 + 55x - 1694
\]

Thus, the simplified product is:
\[
\boxed{x^2 + 55x - 1694}
\]