Adding and subtracting polynomials | Algebra Basics | Khan Academy

Khan Academy
21 Jun 201001:44

Summary

TLDRIn this video, the process of simplifying a polynomial expression is demonstrated. The problem involves the expression '16x + 14 - (3x^2 + x - 9)', and the explanation begins by distributing the negative sign across the terms within the parentheses. The next step involves combining like terms: the quadratic term, linear terms, and constant terms. After simplifying, the final expression is '-3x^2 + 15x + 23'. The video effectively breaks down the steps of polynomial simplification, making it easier to understand for learners.

Takeaways

  • 😀 The expression to simplify is 16x + 14 - (3x^2 + x - 9).
  • 😀 Begin by removing the parentheses without altering the order of operations.
  • 😀 Distribute the negative sign to each term inside the parentheses: -3x^2, -x, and +9.
  • 😀 The highest degree term is -3x^2, as x is raised to the second power.
  • 😀 Combine the x terms: 16x - x = 15x.
  • 😀 The constant terms are 14 and 9, which sum to 23.
  • 😀 The simplified polynomial after combining like terms is -3x^2 + 15x + 23.
  • 😀 When simplifying, always ensure to distribute signs correctly, especially when subtracting terms.
  • 😀 The order of operations is crucial in simplification, especially when parentheses are involved.
  • 😀 The goal is to rewrite the expression as a simplified polynomial by combining like terms.
  • 😀 The final result shows that the expression simplifies into a quadratic form with no like terms left.

Q & A

  • What is the first step in simplifying the expression 16x + 14 - (3x^2 + x - 9)?

    -The first step is to remove the parentheses and distribute the negative sign across the terms inside, which changes the signs of the terms. The expression becomes 16x + 14 - 3x^2 - x + 9.

  • What happens to the term 3x^2 when the negative sign is distributed?

    -When the negative sign is distributed, the positive 3x^2 becomes -3x^2.

  • How do you simplify the linear terms (16x and -x)?

    -You combine the like terms 16x and -x by subtracting 1 from 16, which gives 15x.

  • What happens when you combine the constant terms (14 and 9)?

    -When you combine the constants 14 and 9, you get 23.

  • What is the highest degree term in the expression after simplifying?

    -The highest degree term is -3x^2, which is the second-degree term because x is raised to the power of 2.

  • What is the simplified polynomial after combining all terms?

    -The simplified polynomial is -3x^2 + 15x + 23.

  • Why does the expression 14 + 9 become 23 instead of another number?

    -The expression 14 + 9 is a simple addition of constants, and the sum of 14 and 9 is 23.

  • Why do we distribute the negative sign to each term in the parentheses?

    -We distribute the negative sign to each term to ensure that the signs of the terms inside the parentheses are properly changed, following the rules of algebra.

  • Is the order of operations important when simplifying this expression?

    -Yes, the order of operations is important. First, you simplify inside the parentheses (if needed) and then handle the distribution of the negative sign before combining like terms.

  • What do we call terms that have the same degree, like 16x and -x?

    -Terms that have the same degree are called 'like terms.' In this case, both 16x and -x are linear terms (degree 1), so they can be combined.

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