Question

What expression is equivalent to 3+2(x+4)(x-4)

Answer 1

`\large\boxed{\tt 2x^(2) - 29}`

Explanation:

`\textsf{We are asked what expression is equivalent to the given expression.}`

`\textsf{Note that we can find an equivalent expression by simplifying the expression we}`

`\textsf{already have. We can combine like terms, and simplify by using the \boxed{\textsf{FOIL}} method.}`

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

`\textsf{The FOIL Method is a method that can broken down which tells us how to}`

`\textsf{multiply 2 binomials. Remember that binomials are expressions with 2 terms.}`

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

`\textsf{F - Front terms.}`

`\tt (\ \boxed{\tt4x}+3)(\ \boxed{\tt 3x}+1)`

`\textsf{O - Outer terms.}`

`\tt (\ \boxed{\tt 4x}+3 )(3x+ \boxed{\tt 1} \ )`

`\textsf{I - Inside terms.}`

`\tt (4x+\boxed{\tt3} \ )(\ \boxed{\tt 3x}+1)`

`\textsf{L - Last Terms.}`

`\tt (4x+\boxed{\tt3} \ )(3x+ \boxed{\tt 1} \ )`

`\textsf{We should also use the Distributive Property.}`

`\boxed{ \begin{minipage}{20 em} \\ \underline{\textsf{\large Distributive Property;}} \\ \\ \textsf{Distributive Property is a property that allows us to multiply the term to the \underline{left} of the parentheses into the terms \underline{inside} the parentheses.} \\ \\ \underline{\textsf{\large Example;}} \\ \tt a(b+c) = ab+\tt ac \\ \textsf{A will multiply with b and c as a is the term to the left of the parentheses, and b and c are inside the parentheses.}\end{minipage}}`

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

`\tt 3+2(x+4)(x-4)`

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

`\tt 2(x+4) = 2x + 8`

`\tt 3+(2x+8)(x-4)`

`\underline{\textsf{Use the FOIL Method;}}`

`\textsf{F - Front terms.}`

`\tt (\ \boxed{\tt2x}+8)(\ \boxed{\tt x}-4)`

`\textsf{O - Outer terms.}`

`\tt (\ \boxed{\tt 2x}+8 )(x- \boxed{\tt 4} \ )`

`\textsf{I - Inside terms.}`

`\tt (2x+\boxed{\tt 8} \ )(\ \boxed{\tt x}-4)`

`\textsf{L - Last Terms.}`

`\tt (2x+\boxed{\tt 8} \ )(x- \boxed{\tt 4} \ )`

`\underline{\textsf{We should have;}}`

`\large\boxed{\tt 2x^(2) - 29}`

`\textsf{(After Combining Like Terms)}`