Question

simplify the following expression.
(b + 8)(b + 2)

b² + ?b + \square

Explanation:

Step1: Apply the distributive property (FOIL method)

To expand \((b + 8)(b + 2)\), we use the FOIL method: multiply the First terms, then the Outer terms, then the Inner terms, and finally the Last terms.

• First terms: \(b\times b = b^{2}\)
• Outer terms: \(b\times2 = 2b\)
• Inner terms: \(8\times b = 8b\)
• Last terms: \(8\times2 = 16\)

Step2: Combine like terms

Now, combine the like terms (the terms with \(b\)):
\(2b + 8b = (2 + 8)b = 10b\)

And the constant term is \(16\). So, \((b + 8)(b + 2)=b^{2}+10b + 16\)

Answer:

The coefficient of \(b\) is \(10\) and the constant term is \(16\). So, the expression simplifies to \(b^{2}+10b + 16\), with the missing coefficient being \(10\) and the constant term being \(16\). For the box with the coefficient of \(b\), the answer is \(10\), and for the constant term box, the answer is \(16\).