Answered

Discover new perspectives and gain insights with IDNLearn.com's diverse answers. Get the information you need from our experts, who provide reliable and detailed answers to all your questions.

Simplify the following expression:
[tex]\[ 7mn\left(2m^2 - 4n^2 + 2\right) + mn\left(m^2 - n^2\right) \][/tex]

Sagot :

GinnyAnsweridn
Sure! Let's go step-by-step to simplify the given expression:

[tex]\(7mn(2m^2 - 4n^2 + 2) + mn(m^2 - n^2)\)[/tex]

### Step 1: Distribute [tex]\(mn\)[/tex] inside the parentheses

First, distribute [tex]\(7mn\)[/tex] inside the first parentheses:
[tex]\[7mn(2m^2) - 7mn(4n^2) + 7mn(2)\][/tex]
[tex]\[= 14m^3n - 28mn^3 + 14mn\][/tex]

Now distribute [tex]\(mn\)[/tex] inside the second parentheses:
[tex]\[mn(m^2) - mn(n^2)\][/tex]
[tex]\[= m^3n - mn^3\][/tex]

### Step 2: Combine like terms

Now we have:
[tex]\[14m^3n - 28mn^3 + 14mn + m^3n - mn^3\][/tex]

Combine the terms:
1. [tex]\(m^3n\)[/tex] terms:
[tex]\[14m^3n + m^3n = 15m^3n\][/tex]

2. [tex]\(mn^3\)[/tex] terms:
[tex]\[-28mn^3 - mn^3 = -29mn^3\][/tex]

3. [tex]\(mn\)[/tex] terms:
[tex]\[14mn\][/tex]

### Step 3: Write the final simplified expression:
[tex]\[ 15m^3n - 29mn^3 + 14mn \][/tex]

So, the simplified form of the given expression is:

[tex]\[ 15m^3n - 29mn^3 + 14mn \][/tex]
Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Your search for answers ends at IDNLearn.com. Thanks for visiting, and we look forward to helping you again soon.