To determine the values of [tex]\(A\)[/tex], [tex]\(B\)[/tex], and [tex]\(C\)[/tex] in the table, we need to perform the binomial multiplications as indicated.
Here's the given table for reference:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline & $x$ & 7 \\
\hline $2 x$ & $2 x^2$ & B \\
\hline-3 & A & C \\
\hline
\end{tabular}
\][/tex]
Let’s determine the values one by one:
1. Value of [tex]\(A\)[/tex]:
[tex]\( A \)[/tex] is in the row with [tex]\(-3\)[/tex] and in the column with [tex]\(x\)[/tex]. This means [tex]\( A \)[/tex] is the result of the multiplication [tex]\(-3 \times x\)[/tex]:
[tex]\[
A = -3 \times x = -3x
\][/tex]
2. Value of [tex]\(B\)[/tex]:
[tex]\( B \)[/tex] is in the row with [tex]\(2x\)[/tex] and in the column with [tex]\(7\)[/tex]. This means [tex]\( B \)[/tex] is the result of the multiplication [tex]\(2x \times 7\)[/tex]:
[tex]\[
B = 2x \times 7 = 14x
\][/tex]
3. Value of [tex]\(C\)[/tex]:
[tex]\( C \)[/tex] is in the row with [tex]\(-3\)[/tex] and in the column with [tex]\(7\)[/tex]. This means [tex]\( C \)[/tex] is the result of the multiplication [tex]\(-3 \times 7\)[/tex]:
[tex]\[
C = -3 \times 7 = -21
\][/tex]
Now we have:
[tex]\[
A = -3x, \quad B = 14x, \quad C = -21
\][/tex]
Like terms:
Like terms are terms that contain the same variable raised to the same power. In our case, the like terms are [tex]\(A\)[/tex] and [tex]\(B\)[/tex] because both are terms involving [tex]\(x\)[/tex]. They can be combined if necessary.
Summary:
[tex]\[
A = -3x, \quad B = 14x, \quad C = -21
\][/tex]
The letters from the table that represent like terms are [tex]\(A\)[/tex] and [tex]\(B\)[/tex] because both include the variable [tex]\(x\)[/tex].
