Same x terms

Same x Terms: An Overview

  • The term same x terms refers to those terms in equations that contain the same exponent of ‘x’.
  • These terms are often called like terms as they have the exact same variable part.
  • They can be easily added or subtracted because they represent the same quantities.

Identification of Same x Terms

  • A term with ‘x’ is a same x term with any other term that also has an identical ‘x’.
  • The presence of the same powers of ‘x’ identifies these same x terms or like terms.
  • For instance, in the expression ‘5x^3 + 7x^2 - 3x + 2x^3 -2x - 7’, the terms ‘5x^3’ and ‘2x^3’ are same x terms, and so are ‘-3x’ and ‘-2x’.

Simplifying Expressions Involving Same x Terms

  • A key use of identifying same x terms is to simplify algebraic expressions.
  • To simplify an expression, all like terms are grouped and combined together.
  • They are combined using addition or subtraction, keeping the power of ‘x’ the same.

Step-by-Step Guide for Simplifying Same x Terms

  1. Start by identifying and highlighting all like terms in the algebraic expression.

  2. To combine like terms that are being added, just add their coefficients.

  3. For like terms that are being subtracted, subtract the coefficients.

  4. The combined term keeps the same power of ‘x’.

Examples

  • In the expression ‘3x^2 + 5x - 4x^2 + 2x - 3’, you can combine ‘3x^2’ and ‘-4x^2’ to get ‘-1x^2’. Next combine ‘5x’ and ‘2x’ to get ‘7x’. The simplified expression would thus be ‘-1x^2 + 7x - 3’.

  • For the expression ‘2x^3 - 5x + 7 - 3x^3 + 2x + 6’, combine ‘2x^3’ and ‘-3x^3’ to yield ‘-1x^3’. Then combine ‘-5x’ and ‘2x’ to give ‘-3x’. Finally, add the constants ‘7’ and ‘6’ to get ‘13’. The simplified expression is ‘-1x^3 - 3x + 13’.

Conclusion

  • Understanding same x terms is key in algebra as it allows simplification of complex expressions.
  • This simplification skill is fundamental in solving algebraic problems and equations.