Polynomial Addition and Subtraction Math Example 2

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Example 2

medium
Subtract (5x3−2x2+x)−(3x3+x2−4x+2)(5x^3 - 2x^2 + x) - (3x^3 + x^2 - 4x + 2).

Solution

  1. 1
    Step 1: Distribute the negative sign: 5x3−2x2+x−3x3−x2+4x−25x^3 - 2x^2 + x - 3x^3 - x^2 + 4x - 2.
  2. 2
    Step 2: Group like terms: (5x3−3x3)+(−2x2−x2)+(x+4x)+(−2)(5x^3 - 3x^3) + (-2x^2 - x^2) + (x + 4x) + (-2).
  3. 3
    Step 3: Combine: 2x3−3x2+5x−22x^3 - 3x^2 + 5x - 2.
  4. 4
    Check: At x=1x = 1: (5−2+1)−(3+1−4+2)=4−2=2(5-2+1) - (3+1-4+2) = 4 - 2 = 2 and 2−3+5−2=22-3+5-2 = 2 ✓

Answer

2x3−3x2+5x−22x^3 - 3x^2 + 5x - 2
When subtracting polynomials, distribute the negative sign to every term in the second polynomial before combining like terms. A common mistake is forgetting to change the sign of all terms.

About Polynomial Addition and Subtraction

Adding or subtracting polynomials by combining like terms—terms with the same variable raised to the same power.

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More Polynomial Addition and Subtraction Examples

Example 1 easy

Add [formula].

Example 3 easy

Add [formula].

Example 4 hard

Simplify [formula].

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