Expand 𝑥 plus three multiplied by 𝑥 plus two squared. Give your answer in its simplest form.
𝑥 plus two all squared can be rewritten as 𝑥 plus two multiplied by 𝑥 plus
two. We can expand or multiply out these two brackets using the FOIL method. Multiplying the first terms, 𝑥 multiplied by 𝑥, gives us 𝑥 squared. Multiplying the outside terms, 𝑥 multiplied by two, is two 𝑥. Multiplying the inside terms also gives us two 𝑥. And finally, multiplying the last terms gives us plus four. Two multiplied by two is four.
Grouping or simplifying the like terms gives us 𝑥 squared plus four 𝑥 plus
four. This means that 𝑥 plus two multiplied by 𝑥 plus two or 𝑥 plus two all squared is
equal to 𝑥 squared plus four 𝑥 plus four.
Our next step is to multiply all three of these terms by 𝑥 and then all three of the
terms by three. 𝑥 multiplied by 𝑥 squared is 𝑥 cubed, 𝑥 multiplied by four 𝑥 is four 𝑥 squared,
and 𝑥 multiplied by four is four 𝑥. We then need to multiply all three terms in the second bracket by three. Three multiplied by 𝑥 squared is three 𝑥 squared, three multiplied by four 𝑥 is
12𝑥, and three multiplied by four is equal to 12.
We can simplify this by grouping the 𝑥 squared terms — four 𝑥 squared and three 𝑥
squared — and the two 𝑥 terms — four 𝑥 and 12𝑥. Simplifying this gives us an answer of 𝑥 cubed plus seven 𝑥 squared plus 16𝑥 plus
The expansion of 𝑥 plus three multiplied by 𝑥 plus two all squared in its simplest
form is 𝑥 cubed plus seven 𝑥 squared plus 16𝑥 plus 12.