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.
![### Polynomial Ordering
**Given Problem:**
Write \(-8xy + y^2 + x^2\) in decreasing powers of \(x\).
**Solution:**
To write the given polynomial expression in decreasing powers of \(x\), we need to rearrange the terms so that the terms with higher powers of \(x\) appear first.
The given polynomial is:
\[ -8xy + y^2 + x^2 \]
1. **Identify the powers of \(x\):**
- \(x^2\): Highest power of \(x\)
- \(-8xy\): The power of \(x\) is 1.
- \(y^2\): The power of \(x\) is 0.
2. **Rearrange the terms in decreasing powers of \(x\):**
\[ x^2 - 8xy + y^2 \]
Thus, the polynomial in decreasing powers of \(x\) is:
\[ \boxed{x^2 - 8xy + y^2} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c69c300-2450-4b46-97af-8596007e11b9%2F605cd30d-5c9b-4396-a2be-fcb37f0a04f7%2F4nsg41_processed.png&w=3840&q=75)
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