Answered

Discover new information and get your questions answered with IDNLearn.com. Get prompt and accurate answers to your questions from our experts who are always ready to help.

Select the correct answer.

What is the simplest form of this expression?

[tex]\[ (x+7)(3x-8) \][/tex]

A. [tex]\[ 3x^2 + 2x - 15 \][/tex]

B. [tex]\[ 3x^2 + 29x - 1 \][/tex]

C. [tex]\[ 3x^2 - 29x - 56 \][/tex]

D. [tex]\[ 3x^2 + 13x - 56 \][/tex]

Sagot :

GinnyAnsweridn
To find the simplest form of the expression [tex]\((x + 7)(3x - 8)\)[/tex], we need to use the distributive property, also known as the FOIL method (First, Outer, Inner, Last). Let's expand it step by step:

1. First: Multiply the first terms in each binomial.
- [tex]\(x \cdot 3x = 3x^2\)[/tex]

2. Outer: Multiply the outer terms in the binomials.
- [tex]\(x \cdot -8 = -8x\)[/tex]

3. Inner: Multiply the inner terms in the binomials.
- [tex]\(7 \cdot 3x = 21x\)[/tex]

4. Last: Multiply the last terms in each binomial.
- [tex]\(7 \cdot -8 = -56\)[/tex]

Next, combine these results:
[tex]\[ 3x^2 - 8x + 21x - 56 \][/tex]

Now, combine the like terms ([tex]\(-8x + 21x\)[/tex]):
[tex]\[ 3x^2 + 13x - 56 \][/tex]

Therefore, the simplest form of the expression [tex]\((x + 7)(3x - 8)\)[/tex] is:
[tex]\[ 3x^2 + 13x - 56 \][/tex]

Hence, the correct answer is:
D. [tex]\(3x^2 + 13x - 56\)[/tex]

Answer:

3x² +13x -56

Step-by-step explanation:

You can answer this question using the FOIL method. The FOIL method is used in math to help multiply binomials (*refer to the attached picture to follow the steps*)

Let's follow the FOIL method to simplify the expression:

  • 3x × x = 3x²
  • -8 × x= -8x
  • 7 × 3x= 21x
  • 7 × -8= -56

The rewritten expression should be: 3x² - 8x + 21x -56

Combine like expressions to get the final answer!

3x² +13x -56

Learn more about the FOIL method here: https://brainly.com/question/31177102

View image Pt3222
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.