Question

the table represents the multiplication of two binomials. which letters from the table represent like terms? \

$$\begin{tabular}{|c|c|c|} \\hline & $-2x$ & 3 \\\\ \\hline $4x$ & a & b \\\\ \\hline 1 & c & d \\\\ \\hline \\end{tabular}$$

\bigcirc a and b \bigcirc b and c \bigcirc a and d \bigcirc b and d

Explanation:

Step1: Find expressions for A, B, C, D

To find the expressions for each letter, we use the distributive property (FOIL method) for multiplying binomials. The binomials being multiplied are \((4x + 1)\) and \((-2x + 3)\).

• For \(A\): Multiply \(4x\) and \(-2x\). So, \(A = 4x\times(-2x)= -8x^{2}\)
• For \(B\): Multiply \(4x\) and \(3\). So, \(B = 4x\times3 = 12x\)
• For \(C\): Multiply \(1\) and \(-2x\). So, \(C = 1\times(-2x)= -2x\)
• For \(D\): Multiply \(1\) and \(3\). So, \(D = 1\times3 = 3\)

Step2: Identify like terms

Like terms are terms that have the same variable part (or are constant terms). Let's analyze each option:

• Option A: \(A = -8x^{2}\) and \(B = 12x\). These are not like terms (different exponents on \(x\)).
• Option B: \(B = 12x\) and \(C = -2x\). Both have the variable \(x\) with an exponent of \(1\). So, they are like terms.
• Option C: \(A = -8x^{2}\) and \(D = 3\). Not like terms (one has \(x^{2}\), the other is a constant).
• Option D: \(B = 12x\) and \(D = 3\). Not like terms (one has \(x\), the other is a constant).

Answer:

B. B and C