Question

Use the distributive property to multiply (2x + 3)(x + 7)



2x2 + 17x - 21

2x2 + 11x + 21

2x2 + 17x + 10

2x2 + 17x + 21

Answer 1

To multiply \( (2x + 3)(x + 7) \) using the distributive property (also known as the FOIL method for binomials), we will distribute each term in the first binomial to each term in the second binomial.

1. Distribute \( 2x \) to both terms in \( (x + 7) \):

\[
2x \cdot x = 2x^2
\]
\[
2x \cdot 7 = 14x
\]

2. Distribute \( 3 \) to both terms in \( (x + 7) \):

\[
3 \cdot x = 3x
\]
\[
3 \cdot 7 = 21
\]

Now, combine all the terms together:

\[
2x^2 + 14x + 3x + 21
\]

Combine the like terms (\( 14x + 3x \)):

\[
2x^2 + 17x + 21
\]

So the final result is:

\[
2x^2 + 17x + 21
\]

The correct answer from the options provided is:

**2x² + 17x + 21**