Math Problem Statement
Simplify the following expression with distribution: (4p + 2 + q)(p^2 - 3q + 6)
Solution
Let's solve the given expression step by step using distribution.
The given expression is:
We will use the distributive property, multiplying each term from the first binomial by each term from the second binomial.
- Multiply by each term in :
- Multiply by each term in :
- Multiply by each term in :
Now, combine all these terms together:
Simplifying, the terms involving cancel out, so we are left with:
This matches the third option in the image:
Would you like more details on any step? Here are some additional questions to explore this further:
- How would the expression change if one of the terms was squared?
- Can this expression be factored after simplification?
- What happens if we change the order of multiplication (commutativity)?
- How would you approach this problem if it involved more variables?
- What is the importance of grouping like terms in simplifying polynomial expressions?
Tip: Always keep track of positive and negative signs when distributing across multiple terms to avoid errors.
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Math Problem Analysis
Mathematical Concepts
Polynomial Multiplication
Distributive Property
Algebra
Formulas
(a+b)(c+d) = ac + ad + bc + bd
Theorems
-
Suitable Grade Level
Grades 9-10