1 Simplify the polynomial. Answer m \( \begin{array}{l}(x+2)(x+7)\end{array} \)

To simplify the polynomial \( (x+2)(x+7) \), you can use the distributive property, also known as the FOIL method for binomials. Multiply the first terms, outer terms, inner terms, and last terms together: First: \( x \cdot x = x^2 \) Outer: \( x \cdot 7 = 7x \) Inner: \( 2 \cdot x = 2x \) Last: \( 2 \cdot 7 = 14 \) Now, combine like terms: \( x^2 + 7x + 2x + 14 = x^2 + 9x + 14 \) So, the simplified form of the polynomial is \( x^2 + 9x + 14 \). To keep things fun, think of binomials like a couple of roommates sharing a tiny apartment. When they combine their space (the terms), they have more room for activities (the resulting terms of \( x^2 + 9x + 14 \))! The more they work together, the more they can achieve in the living room of algebra. Now, consider that simplifying polynomials isn't just about crunching numbers—it’s a bit of a magic trick! There are common mistakes like forgetting to distribute correctly or mixing up signs. Always double-check your work and remember to keep an eye on those pesky negative signs; they can sneak in and throw off your final answer!