Questions: 1) (4x^2y-xy^2+5)+(-6x^2y-1) 2) (2m^4-n-5n+1)+(m+m^4-6)

1) (4x^2y-xy^2+5)+(-6x^2y-1) 2) (2m^4-n-5n+1)+(m+m^4-6)
Transcript text: 1) $\left(4 x^{2} y-x y^{2}+5\right)+\left(-6 x^{2} y-1\right)$ 2) $\left(2 m^{4}-n-5 n+1\right)+\left(m+m^{4}-6\right)$
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Solution

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Solution Steps

Step 1: Identify Like Terms

For each polynomial expression, identify the like terms that can be combined.

  1. Expression: \((4x^2y - xy^2 + 5) + (-6x^2y - 1)\)
  • Like terms: \(4x^2y\) and \(-6x^2y\)
  • Constant terms: \(5\) and \(-1\)
  1. Expression: \((2m^4 - n - 5n + 1) + (m + m^4 - 6)\)
  • Like terms: \(2m^4\) and \(m^4\); \(-n\) and \(-5n\)
  • Constant terms: \(1\) and \(-6\)
Step 2: Combine Like Terms

Combine the like terms identified in Step 1.

  1. \((4x^2y - xy^2 + 5) + (-6x^2y - 1)\)
  • Combine \(4x^2y\) and \(-6x^2y\): \((4 - 6)x^2y = -2x^2y\)
  • Combine constants: \(5 - 1 = 4\)

Resulting expression: \(-2x^2y - xy^2 + 4\)

  1. \((2m^4 - n - 5n + 1) + (m + m^4 - 6)\)
  • Combine \(2m^4\) and \(m^4\): \((2 + 1)m^4 = 3m^4\)
  • Combine \(-n\) and \(-5n\): \((-1 - 5)n = -6n\)
  • Combine constants: \(1 - 6 = -5\)

Resulting expression: \(3m^4 - 6n + m - 5\)

Final Answer

  1. \(\boxed{-2x^2y - xy^2 + 4}\)

  2. \(\boxed{3m^4 - 6n + m - 5}\)

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