Question

How do you foil $ {\left( {x + 3} \right)^2} $ ?

Answer 1

Hint: In this question we need to solve the expression $ {\left( {x + 3} \right)^2} $ using the FOIL method. Thus, we know that letters in FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial, Outer means multiply the outermost terms in the product, Inner means multiply the innermost terms, and Last means multiply the terms which occur last in each binomial. By using this method we will solve the given expression and evaluate it to determine the required solution.

Complete step-by-step answer:
First let us rewrite the expression as $ \left( {x + 3} \right)\left( {x + 3} \right) $ .
Now, let us solve the expression using FOIL’s method. The letters in FOIL stands for First, Outer, Inner, Last.
First means multiply the terms which occur first in each binomial,
 $ x \times x = {x^2} $
Outer means multiply the outermost terms in the product,
 $ x \times 3 = 3x $
Inner means multiply the innermost terms,
 $ x \times 3 = 3x $
Last means multiply the terms which occur last in each binomial,
 $ 3 \times 3 = 9 $
Therefore, we have,
 $ \left( {x + 3} \right)\left( {x + 3} \right) = {x^2} + 3x + 3x + 9 $
Hence, $ {\left( {x + 3} \right)^2} = {x^2} + 6x + 9 $
So, the correct answer is “ $ {x^2} + 6x + 9 $ ”.

Note: We know that the distributive property is the ability of one operation to distribute over another operation contained inside a set of parenthesis. Most commonly, this refers to the property of multiplication distributive over addition or subtraction, such that $ a\left( {b + c} \right) = ab + ac $ . When we say that multiplication distributes over addition, it means we can distribute the multiplicative factor outside the set of parentheses to each item inside, and then add the results.
If the expression is in the form $ a\left( {b + c} \right) = ab + ac $ then, we can use the distributive property but here the expression is in the form $ \left( {x + 3} \right)\left( {x + 3} \right) $ , in such cases we will use the FOIL method. FOIL method is a technique for distributing two binomials.