Polynomial Addition and Subtraction Math Example 4

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Example 4

hard
Simplify (x4+2x2−3)−(2x4−x3+2x2+1)(x^4 + 2x^2 - 3) - (2x^4 - x^3 + 2x^2 + 1).

Solution

  1. 1
    Distribute: x4+2x2−3−2x4+x3−2x2−1x^4 + 2x^2 - 3 - 2x^4 + x^3 - 2x^2 - 1.
  2. 2
    Combine: −x4+x3+0x2−4=−x4+x3−4-x^4 + x^3 + 0x^2 - 4 = -x^4 + x^3 - 4.

Answer

−x4+x3−4-x^4 + x^3 - 4
Higher-degree polynomial subtraction follows the same rules — distribute the negative, then combine like terms. Notice that 2x2−2x2=02x^2 - 2x^2 = 0, eliminating that term entirely.

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 2 medium

Subtract [formula].

Example 3 easy

Add [formula].

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