Math Problem Statement

Find the sum of 6, x, squared, minus, 36x 2 −3 and 8, x, squared, minus, 5, x, minus, 18x 2 −5x−1.

Solution

To solve this, we are adding two algebraic expressions:

  1. 6x236x36x^2 - 36x - 3
  2. 8x25x18x^2 - 5x - 1

Now, let's add the like terms:

  • For the x2x^2-terms:
    6x2+8x2=14x26x^2 + 8x^2 = 14x^2

  • For the xx-terms:
    36x5x=41x-36x - 5x = -41x

  • For the constant terms:
    31=4-3 - 1 = -4

So, the sum of the two expressions is:

14x241x414x^2 - 41x - 4

Would you like more details or further explanation on any step?

Here are 5 questions related to this:

  1. How do you combine like terms in algebraic expressions?
  2. What is the difference between coefficients and constants in polynomials?
  3. How do you factor quadratic expressions like 14x241x414x^2 - 41x - 4?
  4. Can quadratic equations always be simplified further?
  5. What is the general form of a quadratic expression?

Tip: Always align like terms when adding or subtracting polynomials to simplify your work!

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomials
Like Terms

Formulas

Adding like terms: ax^n + bx^n = (a+b)x^n

Theorems

Polynomial Addition

Suitable Grade Level

Grades 8-10