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
-
Start by identifying and highlighting all like terms in the algebraic expression.
-
To combine like terms that are being added, just add their coefficients.
-
For like terms that are being subtracted, subtract the coefficients.
-
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.