Math Problem Statement

Simplify the expression 4y^4(2xy - 2y^2).

Solution

The expression in the image is:

4y4(2xy2y2)4y^4(2xy - 2y^2)

Let's simplify this step by step using the distributive property. We will multiply each term inside the parentheses by 4y44y^4.

  1. First, distribute 4y44y^4 to 2xy2xy: 4y4×2xy=8xy54y^4 \times 2xy = 8xy^5

  2. Then, distribute 4y44y^4 to 2y2-2y^2: 4y4×2y2=8y64y^4 \times -2y^2 = -8y^6

Now, combining these, the simplified expression is:

8xy58y68xy^5 - 8y^6

Would you like any further clarifications or details on this solution? Here are some related questions:

  1. How do we apply the distributive property in algebraic expressions?
  2. What are the general rules for multiplying exponents in algebra?
  3. How does this problem relate to polynomial multiplication?
  4. Can this expression be factored further?
  5. What happens if we plug in specific values for xx and yy?

Tip: When multiplying terms with exponents, always remember to add the exponents if the bases are the same!

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Math Problem Analysis

Mathematical Concepts

Algebra
Distributive Property
Exponents

Formulas

a(b + c) = ab + ac
Multiplication of Exponents: x^a * x^b = x^(a + b)

Theorems

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Suitable Grade Level

Grades 8-10