Question

(10 + 13)(2 + 7y)
Which expression is equivalent to the expression above?
20 + 70y
23 + 9y
26 + 91y
46 + 161y

Answer 1

To simplify the expression (10 + 13)(2 + 7y), we will use the distributive property (also known as the FOIL method for binomials).

1. **Multiply the first terms:**
\(10 \times 2 = 20\)

2. **Multiply the outer terms:**
\(10 \times 7y = 70y\)

3. **Multiply the inner terms:**
\(13 \times 2 = 26\)

4. **Multiply the last terms:**
\(13 \times 7y = 91y\)

Now, we combine all these results:

\[
20 + 70y + 26 + 91y
\]

Next, we combine the constant terms (20 and 26) and the variable terms (70y and 91y):

\[
(20 + 26) + (70y + 91y) = 46 + 161y
\]

Thus, the expression \((10 + 13)(2 + 7y)\) is equivalent to:

\[
\boxed{46 + 161y}
\]