Question

Which is the product of left-parenthesis 7 plus 4 x right-parenthesis left-parenthesis 2 minus 9 x right-parenthesis?

Answer options with 4 options
A.
14 minus 36 x squared

B.
14 plus 71 x minus 36 x squared

C.
28 plus 8 x minus 18 x squared

D.
14 minus 55 x minus 36 x squared

Answer 1

To find the product of \((7 + 4x)(2 - 9x)\), we can use the distributive property (also known as the FOIL method for binomials).

1. Multiply the first terms:
\[
7 \cdot 2 = 14
\]

2. Multiply the outer terms:
\[
7 \cdot (-9x) = -63x
\]

3. Multiply the inner terms:
\[
4x \cdot 2 = 8x
\]

4. Multiply the last terms:
\[
4x \cdot (-9x) = -36x^2
\]

Now we combine all these results:
\[
14 - 63x + 8x - 36x^2
\]

Combine like terms (\(-63x + 8x\)):
\[
14 - 55x - 36x^2
\]

The final result is:
\[
14 - 55x - 36x^2
\]

Therefore, the correct answer is:
**D. \(14 - 55x - 36x^2\)**.