Question

Expand and simplify 2(x+7) + 3(x+1)

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Answer 1

`\large\boxed{\tt 5x + 17}`

Explanation:

`\textsf{We are asked to expand, and simplifying 2 expressions.}`

`\textsf{We should understand what the question is asking from us first.}`

`\large\underline{\textsf{What are Expressions?}}`

`\textsf{Expressions are statements that are made up of 2 or more terms. Such expressions}`

`\textsf{should incl\textsf{u}de an operation as well. (+, -, } \tt *, \tt / )`

`\large\underline{\textsf{What is Expanding?}}`

`\textsf{Expanding in Mathematics involves with the Distributive Property, where an}`

`\textsf{expression is expanded to further simplify the expression.}`

`\underline{\textsf{How are we able to expand expressions?}}`

`\textsf{Expanding Expressions has to incl\textsf{u}de the Distributive Property.}`

`\large\underline{\textsf{What is the Distributive Property?}}`

`\boxed{\begin{minipage}{23 em} \\ \underline{\textsf{\large Distributive Property;}} \\ \\ \textsf{Distributive Property is a property that allows us to multiply the term to the left of the parentheses into the terms inside the parentheses.} \\ \\ \underline{\textsf{\large Example;}} \\ \tt a(b+c)=ab+ac \\ \textsf{For this example, a will multiply with the terms b and c.}\end{minipage}}`

`\textsf{Even though Distributive Property is mainly used for Distributing 1 term}`

`\textsf{expressions, it's commonly used for distributing binomials as well, which involves}`

`\textsf{the FOIL Method.}`

`\large\underline{\textsf{What is the FOIL Method?}}`

`\textsf{The FOIL Method is a very useful method that tells us step-by-step how to}`

`\textsf{multiply 2 binomials. For any polynomial with 2 or more terms, apply the idea}`

`\textsf{of the FOIL method, however using it more than once.}`

`\underline{\textsf{FOIL Means;}}`

`\textsf{F - Front Terms.}`

`\tt ( \ \boxed{\tt x} + 1 )( \ \boxed{\tt x} - 1 )`

`\textsf{O - Outer Terms.}`

`\tt ( \ \boxed{\tt x} + 1 )( x - \boxed{\tt 1} \ )`

`\textsf{I - Inside Terms}`

`\tt (x + \boxed{\tt 1} \ )( \ \boxed{\tt x} - 1 )`

`\textsf{L - Last Terms.}`

`\tt (x + \boxed{\tt 1} \ )( x - \boxed{\tt 1} \ )`

`\large\underline{\textsf{What is Simplifying?}}`

`\textsf{Simplifying anything related to mathematics means to reduce, and to make the}`

`\textsf{final answer much simpler and clean.}`

`\underline{\textsf{What are some ways that we can Simplify?}}`

• 
  `\textsf{Combining Like Terms,}`
• 
  `\textsf{Distributive Property,}`
• 
  `\textsf{Reducing Radicals/Fractions.}`

`\large\underline{\textsf{Solving;}}`

`\textsf{We are given 2 expressions where we should use the Distributive Property to}`

`\textsf{expand both of the expressions. Lastly, simplify the expression by combining any}`

`\textsf{like terms necessary.}`

`\tt 2(x+7) + 3(x+1)`

`\underline{\textsf{Use the Distributive Property;}}`

`\tt 2(x+7) = (2(x)) + (2(7)) = 2x+14`

`\tt 3(x+1) = (3(x)) + (3(1)) = 3x+3`

`\tt 2(x+7) + 3(x+1) = 2x+14+3x+3`

`\underline{\textsf{Combine Like Terms;}}`

`\tt \boxed{\tt 2x} + 14 + \boxed{\tt 3x} + 3`

`\tt 5x + \boxed{\tt 14} + \boxed{\tt 3}`

`\large\boxed{\tt 5x + 17}`

Answer 2

`5x + 17`

Explanation:

`2(x + 7) + 3(x + 1)`

Multiply every term inside the bracket by the term on the outside:

`2x + 14 + 3x + 3`

Collect like terms:

`5x + 17`