Find solutions to your questions with the help of IDNLearn.com's expert community. Our platform is designed to provide accurate and comprehensive answers to any questions you may have.

Simplify the following expression:

[tex]\[ 2(a - b) + 4 \left( \frac{1}{2a} a + 6b \right) \][/tex]


Sagot :

Certainly! Let's simplify the given expression step-by-step.

### Given Expression:
[tex]\[ 2(a - b) + 4\left(\frac{1}{2a} a + 6b\right) \][/tex]

### Step 1: Simplify the expression inside the parentheses
First, let's look at the term inside parentheses:
[tex]\[ \frac{1}{2a} a + 6b \][/tex]

Notice that [tex]\(\frac{1}{2a} a\)[/tex] simplifies directly because the [tex]\(a\)[/tex] in the numerator and denominator cancel out:
[tex]\[ \frac{1}{2a} a = \frac{a}{2a} = \frac{1}{2} \][/tex]

So, now we have:
[tex]\[ \frac{1}{2} + 6b \][/tex]

### Step 2: Distribute the 4 into the expression inside the parentheses
Next, distribute the 4:
[tex]\[ 4 \left( \frac{1}{2} + 6b \right) = 4 \cdot \frac{1}{2} + 4 \cdot 6b \][/tex]
[tex]\[ = 2 + 24b \][/tex]

### Step 3: Combine with the first part of the expression
Bringing everything together, we now have:
[tex]\[ 2(a - b) + 2 + 24b \][/tex]

### Step 4: Distribute the 2 into the first part of the expression
Next, distribute the 2:
[tex]\[ 2(a - b) = 2a - 2b \][/tex]

So now we combine everything:
[tex]\[ 2a - 2b + 2 + 24b \][/tex]

### Step 5: Combine like terms
Now, let's combine the like terms:
- Combine the [tex]\( -2b \)[/tex] and [tex]\( 24b \)[/tex] terms:
[tex]\[ -2b + 24b = 22b \][/tex]
- We add the constant term 2.

Thus, the simplified form is:
[tex]\[ 2a + 22b + 2 \][/tex]

So the final simplified expression is:
[tex]\[ 2a + 22b + 2 \][/tex]