Question

Choose the expression that is equivalent to 12 x plus 3 y.
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Part 1
A.3 left parenthesis 4 x plus 3 y right parenthesis
3 left parenthesis 4 x plus 3 y right parenthesis
B.3 left parenthesis 4 x plus y right parenthesis
3 left parenthesis 4 x plus y right parenthesis
C.15 xy
15 xy
D.3 left parenthesis 9 x plus y right parenthesis
3 left parenthesis 9 x plus y right parenthesis

Answer 1

To find an expression equivalent to \( 12x + 3y \), we can factor out a common factor from both terms.

The common factor of \( 12x \) and \( 3y \) is \( 3 \):

\[
12x + 3y = 3(4x) + 3(1y) = 3(4x + y)
\]

Now let's evaluate the options provided:

A. \( 3(4x + 3y) \)
B. \( 3(4x + y) \)
C. \( 15xy \)
D. \( 3(9x + y) \)

The expression that matches our factorization \( 3(4x + y) \) is:

**B. \( 3(4x + y) \)**

So, the answer is **B**.