How to add and subtract like terms to simplify polynomials
Like terms have the same variable (letter) and same exponent
Adding and subtracting like terms is also known as combining like terms.
Like terms are variables that have the same letter and same exponent.
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We combine them by adding or subtracting the coefficients (the number in front of the letter). The exponents will stay the same after adding or subtracting like terms. Remember that ???x??? is also equal to ???1x^1???.
How to add and subtract like terms (combine like terms)
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Simplifying polynomials by combining like terms
Example
Simplify the expression.
???2x+x-3x+5x???
All of these terms have the same variable ???x??? with the same exponent ???1??? so we’ll add all of the coefficients together.
???(2+1-3+5)x???
???(3-3+5)x???
???5x???
Let’s try another example of adding and subtracting like terms.
Like terms are variables that have the same letter and same exponent.
Example
Simplify the expression.
???x-3x^2+4x+7x^2???
Start by grouping terms together that have the same variable and exponent combination.
???x+4x+7x^2-3x^2???
Combine the ???x??? terms.
???(1+4)x+7x^2-3x^2???
???5x+7x^2-3x^2???
Combine the ???x^2??? terms.
???5x+(7-3)x^2???
???5x+4x^2???
