Math Problem Statement

Simplify the expression 7x^2 - 9x + 5 - 7(x^2 + 1)

Solution

The given expression is:

7x29x+57(x2+1)7x^2 - 9x + 5 - 7(x^2 + 1)

Let's simplify the expression step-by-step.

Step 1: Distribute the 7-7 across the terms inside the parentheses

7x29x+57(x2)7(1)7x^2 - 9x + 5 - 7(x^2) - 7(1) =7x29x+57x27= 7x^2 - 9x + 5 - 7x^2 - 7

Step 2: Combine like terms

(7x27x2)+(9x)+(57)(7x^2 - 7x^2) + (-9x) + (5 - 7) =0x29x2= 0x^2 - 9x - 2

Step 3: Simplify the expression

=9x2= -9x - 2

So, the simplified expression is:

9x2\boxed{-9x - 2}

Would you like more details or have any questions?

Here are some related questions you might find helpful:

  1. How do you distribute terms in an algebraic expression?
  2. What does it mean to combine like terms?
  3. How do you factor out common terms from an algebraic expression?
  4. What is the role of negative signs in distribution?
  5. How do you solve equations once they are simplified?

Tip: Always check for like terms after distributing to ensure you've simplified the expression completely.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplification
Distribution
Combining Like Terms

Formulas

Distribution of constants over addition: a(b + c) = ab + ac

Theorems

Distributive Property

Suitable Grade Level

Grades 7-9