Math Problem Statement

solve

-8ab(x^2 + y^a - 4)

Solution

The given expression to multiply is:

8ab(x2+ya4)-8ab \left( x^2 + y^a - 4 \right)

Now, distributing the 8ab-8ab term across the terms inside the parentheses:

  1. 8abx2=8abx2-8ab \cdot x^2 = -8abx^2
  2. 8abya=8abya-8ab \cdot y^a = -8aby^a
  3. 8ab(4)=32ab-8ab \cdot (-4) = 32ab

Putting all these together:

8abx28abya+32ab-8abx^2 - 8aby^a + 32ab

The final result is:

8abx28abya+32ab-8abx^2 - 8aby^a + 32ab

Would you like more details or explanations on any step?

Here are 5 related questions you might find interesting:

  1. How can you distribute more complex terms?
  2. What happens when we factor out common terms?
  3. How does this method apply in polynomial multiplication?
  4. What are some special cases in multiplication of binomials or trinomials?
  5. Can you solve similar expressions with exponents that are fractions?

Tip: Always check for common factors after expanding terms to simplify the expression further.

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Multiplication
Distributive Property

Formulas

Distributive property: a(b + c) = ab + ac

Theorems

Distributive Property

Suitable Grade Level

Grades 8-10