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(16x+8x^2y-7xy^2+9y)+(5xy^2+10x^2y+x-7y)

2 min read Jun 16, 2024
(16x+8x^2y-7xy^2+9y)+(5xy^2+10x^2y+x-7y)

Simplifying Polynomial Expressions

In mathematics, simplifying polynomial expressions is a fundamental skill. We can combine like terms to make expressions easier to understand and work with. Let's explore how to simplify the following expression:

(16x + 8x^2y - 7xy^2 + 9y) + (5xy^2 + 10x^2y + x - 7y)

Step 1: Identify Like Terms

Like terms are terms that have the same variables and exponents. In our expression, we can group the terms as follows:

  • x terms: 16x + x
  • x^2y terms: 8x^2y + 10x^2y
  • xy^2 terms: -7xy^2 + 5xy^2
  • y terms: 9y - 7y

Step 2: Combine Like Terms

Now, we can combine the coefficients of the like terms:

  • 16x + x = 17x
  • 8x^2y + 10x^2y = 18x^2y
  • -7xy^2 + 5xy^2 = -2xy^2
  • 9y - 7y = 2y

Step 3: Write the Simplified Expression

Finally, we combine the simplified terms to get the simplified expression:

**(16x + 8x^2y - 7xy^2 + 9y) + (5xy^2 + 10x^2y + x - 7y) = 18x^2y - 2xy^2 + 17x + 2y

Therefore, the simplified form of the given expression is 18x^2y - 2xy^2 + 17x + 2y.

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