Simplify: start fraction, minus, 28, y, to the power 5 , plus, 12, y, to the power 4 , plus, 12, y, cubed, divided by, minus, 4, y, squared, end fraction
−4y
2

−28y
5
+12y
4
+12y
3

​

To simplify the expression

\[
\frac{-28y^5 + 12y^4 + 12y^3}{-4y^2}
\]

we can divide each term in the numerator by \(-4y^2\):

1. **First term:** 
   \[
   \frac{-28y^5}{-4y^2} = 7y^3
   \]

2. **Second term:**
   \[
   \frac{12y^4}{-4y^2} = -3y^2
   \]

3. **Third term:**
   \[
   \frac{12y^3}{-4y^2} = -3y
   \]

Putting these together, the simplified expression is:

\[
7y^3 - 3y^2 - 3y
\]

Would you like further details on each step or have any questions?

---

Here are related questions you might find helpful:
1. How do you simplify expressions with variables in both the numerator and denominator?
2. What are common techniques for factoring polynomial expressions?
3. How do you handle negative exponents in fractions?
4. What is the process for dividing a polynomial by a monomial?
5. How can you use polynomial division in real-world applications?

**Tip:** When simplifying fractions, always check if each term in the numerator can be divided by the denominator for a quicker solution.

Simplify: \(\frac{-28y^5 + 12y^4 + 12y^3}{-4y^2}\)

This page provides a detailed solution to simplifying the polynomial expression \(-28y^5 + 12y^4 + 12y^3\) over \(-4y^2\), using core algebraic concepts including properties of exponents and polynomial division. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation