Math Problem Statement

Simplify the expression: -9(-6p^2 - 8) + -9(-2 - 8p)

Solution

The given expression is:

9(6p2+(8))+(9)(28p)-9(-6p^2 + (-8)) + (-9)(-2 - 8p)

Let's simplify this step by step.

Step 1: Distribute the 9-9 to the terms inside both parentheses

  1. For the first term 9(6p2+(8))-9(-6p^2 + (-8)): 9×6p2=54p2-9 \times -6p^2 = 54p^2 9×8=72-9 \times -8 = 72 So, the first term simplifies to: 54p2+7254p^2 + 72

  2. For the second term 9(28p)-9(-2 - 8p): 9×2=18-9 \times -2 = 18 9×8p=72p-9 \times -8p = 72p So, the second term simplifies to: 18+72p18 + 72p

Step 2: Combine all the terms

Now we combine both results: 54p2+72+18+72p54p^2 + 72 + 18 + 72p

Step 3: Simplify the constant terms

54p2+72p+(72+18)54p^2 + 72p + (72 + 18) 54p2+72p+9054p^2 + 72p + 90

Thus, the simplified expression is:

54p2+72p+9054p^2 + 72p + 90

Would you like more details or have any other questions? Here are five related questions:

  1. How do you simplify more complex polynomial expressions?
  2. What is the distributive property, and why is it important in simplification?
  3. Can this expression be factored further? If so, how?
  4. What is the difference between like terms and unlike terms in algebra?
  5. How would the simplification change if the expression had subtraction or division?

Tip: Always combine like terms after distributing, to keep the expression as simple as possible!

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Math Problem Analysis

Mathematical Concepts

Algebra
Distributive Property
Simplification
Polynomials

Formulas

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

Theorems

Distributive Property

Suitable Grade Level

Grades 7-10