Question
What is the simplest form of this expression?
(x + 7)(3x − 8)
A.
3x2 + 2x − 15
B.
3x2 + 29x − 1
C.
3x2 − 29x − 56
D.
3x2 + 13x – 56
(x + 7)(3x − 8)
A.
3x2 + 2x − 15
B.
3x2 + 29x − 1
C.
3x2 − 29x − 56
D.
3x2 + 13x – 56
Answers
GPT-4o mini
To simplify the expression \((x + 7)(3x - 8)\), we will use the distributive property (also known as the FOIL method for binomials).
1. Distributing the first terms: \(x \cdot 3x = 3x^2\)
2. Distributing the outer terms: \(x \cdot (-8) = -8x\)
3. Distributing the inner terms: \(7 \cdot 3x = 21x\)
4. Distributing the last terms: \(7 \cdot (-8) = -56\)
Now, we combine all of these products:
\[
3x^2 - 8x + 21x - 56
\]
Next, we combine the like terms \(-8x\) and \(21x\):
\[
3x^2 + (21x - 8x) - 56 = 3x^2 + 13x - 56
\]
Thus, the simplified expression is:
\[
3x^2 + 13x - 56
\]
The correct answer is:
**D. \(3x^2 + 13x - 56\)**.
1. Distributing the first terms: \(x \cdot 3x = 3x^2\)
2. Distributing the outer terms: \(x \cdot (-8) = -8x\)
3. Distributing the inner terms: \(7 \cdot 3x = 21x\)
4. Distributing the last terms: \(7 \cdot (-8) = -56\)
Now, we combine all of these products:
\[
3x^2 - 8x + 21x - 56
\]
Next, we combine the like terms \(-8x\) and \(21x\):
\[
3x^2 + (21x - 8x) - 56 = 3x^2 + 13x - 56
\]
Thus, the simplified expression is:
\[
3x^2 + 13x - 56
\]
The correct answer is:
**D. \(3x^2 + 13x - 56\)**.