Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
![### Solving Polynomial Expressions
#### Question:
Which expression is equivalent to \((2x^2 + 3)(x + 4)\)?
#### Options:
**A.** \(2x^3 + 12\)
**B.** \(2x^2 + 11x + 12\)
**C.** \(2x^3 + 6x^2 + 4x + 12\)
**D.** \(2x^3 + 8x^2 + 3x + 12\)
### Explanation:
To find the equivalent expression, we need to expand the polynomial \((2x^2 + 3)(x + 4)\) using the distributive property.
1. **Distribute \(2x^2\) across \(x + 4\)**:
\[
2x^2 \cdot x + 2x^2 \cdot 4 = 2x^3 + 8x^2
\]
2. **Distribute \(3\) across \(x + 4\)**:
\[
3 \cdot x + 3 \cdot 4 = 3x + 12
\]
3. **Combine all the terms**:
\[
2x^3 + 8x^2 + 3x + 12
\]
### Conclusion:
The expression equivalent to \((2x^2 + 3)(x + 4)\) is:
**D.** \(2x^3 + 8x^2 + 3x + 12\).
This approach ensures that all terms are accounted for and properly combined to form the correct polynomial expression.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea59d659-13ea-4073-88ed-0121204c1b21%2Fdbd498f9-2208-48e1-ad77-797d38e633b9%2Frk6uy5k_processed.jpeg&w=3840&q=75)
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