At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
To simplify the expression \( 4x(x + 1) - (3x - 8)(x + 4) \), let's break it down step-by-step.
### Step 1: Expand the first part \( 4x(x + 1) \)
Expanding this expression:
[tex]\[ 4x(x + 1) = 4x \cdot x + 4x \cdot 1 = 4x^2 + 4x \][/tex]
### Step 2: Expand the second part \( (3x - 8)(x + 4) \)
Expanding this expression:
[tex]\[ (3x - 8)(x + 4) = 3x \cdot x + 3x \cdot 4 - 8 \cdot x - 8 \cdot 4 \][/tex]
[tex]\[ = 3x^2 + 12x - 8x - 32 \][/tex]
[tex]\[ = 3x^2 + 4x - 32 \][/tex]
### Step 3: Subtract the second expanded expression from the first expanded expression
Now, we subtract the expanded form of the second expression from the expanded form of the first expression:
[tex]\[ 4x^2 + 4x - (3x^2 + 4x - 32) \][/tex]
[tex]\[ = 4x^2 + 4x - 3x^2 - 4x + 32 \][/tex]
### Step 4: Simplify the resulting expression
Combining like terms:
[tex]\[ = (4x^2 - 3x^2) + (4x - 4x) + 32 \][/tex]
[tex]\[ = x^2 + 0 + 32 \][/tex]
[tex]\[ = x^2 + 32 \][/tex]
### Step 5: Classify the resulting polynomial
We observe that the simplified expression is \( x^2 + 32 \). This is a quadratic polynomial because the highest degree of \( x \) is 2. The expression has two terms: \( x^2 \) and \( 32 \). Therefore, it is a binomial (a polynomial containing exactly two terms).
Thus, the resulting polynomial is a quadratic binomial.
The answer is:
B. quadratic binomial
### Step 1: Expand the first part \( 4x(x + 1) \)
Expanding this expression:
[tex]\[ 4x(x + 1) = 4x \cdot x + 4x \cdot 1 = 4x^2 + 4x \][/tex]
### Step 2: Expand the second part \( (3x - 8)(x + 4) \)
Expanding this expression:
[tex]\[ (3x - 8)(x + 4) = 3x \cdot x + 3x \cdot 4 - 8 \cdot x - 8 \cdot 4 \][/tex]
[tex]\[ = 3x^2 + 12x - 8x - 32 \][/tex]
[tex]\[ = 3x^2 + 4x - 32 \][/tex]
### Step 3: Subtract the second expanded expression from the first expanded expression
Now, we subtract the expanded form of the second expression from the expanded form of the first expression:
[tex]\[ 4x^2 + 4x - (3x^2 + 4x - 32) \][/tex]
[tex]\[ = 4x^2 + 4x - 3x^2 - 4x + 32 \][/tex]
### Step 4: Simplify the resulting expression
Combining like terms:
[tex]\[ = (4x^2 - 3x^2) + (4x - 4x) + 32 \][/tex]
[tex]\[ = x^2 + 0 + 32 \][/tex]
[tex]\[ = x^2 + 32 \][/tex]
### Step 5: Classify the resulting polynomial
We observe that the simplified expression is \( x^2 + 32 \). This is a quadratic polynomial because the highest degree of \( x \) is 2. The expression has two terms: \( x^2 \) and \( 32 \). Therefore, it is a binomial (a polynomial containing exactly two terms).
Thus, the resulting polynomial is a quadratic binomial.
The answer is:
B. quadratic binomial
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.