Question

How do you foil \[\left( x+8 \right)\left( x-8 \right)\].

Answer 1

Hint: First we should know what it means to foil an expression. For an expression of the form \[(a+b)(c+d)\]. FOIL involves carrying out the below operations in the following order:
Operation 1: product of the First terms – product of the first terms of two brackets \[ac\].
Operation 2: product of the Outside terms – product of the first term of first bracket and second term of second bracket \[ad\].
Operation 3: product of Inside terms – product of the second term of first bracket and first term of second bracket \[bc\].
Operation 4: product of Last terms – product of the second terms of two brackets \[bd\].
And at last, adding the results of the above four operations.

Complete step by step answer:
We are given the expression \[\left( x+8 \right)\left( x-8 \right)\], we are asked to FOIL the given expression.
To foil an expression, we have to carry out some operations, we will do them for the given expression

First operation is to product of the first terms of two brackets,
\[\Rightarrow x\times x={{x}^{2}}\]

Second operation is product of the first term of first bracket and second term of second bracket
\[\Rightarrow x\times (-8)=-8{{x}^{{}}}\]

Third operation is product of the second term of first bracket and first term of second bracket
\[\Rightarrow 8\times x=8{{x}^{{}}}\]

Fourth operation is product of the second terms of two brackets
\[\Rightarrow 8\times (-8)=-64\]

Finally, we have to add the results of the above four operation, by doing this we get
\[\begin{align}
  & \Rightarrow {{x}^{2}}-8x+8x-64 \\
 & \Rightarrow {{x}^{2}}-64 \\
\end{align}\]

Note: As the given expression is of the form \[(a+b)(a-b)\]. We can reduce the number of steps by using its expansion as \[{{a}^{2}}-{{b}^{2}}\], to simplify the given expression. Here \[a=x\And b=8\], substituting the values, we get
\[\Rightarrow {{x}^{2}}-64\]
We are getting the same result from both FOIL, and the expansion.