like terms
Like terms are terms in algebraic expressions that have the same variable(s) raised to the same power
Like terms are terms in algebraic expressions that have the same variable(s) raised to the same power. In other words, they have identical variables and exponents. By combining like terms, you can simplify algebraic expressions and solve equations more efficiently.
To understand like terms, let’s consider an example:
3x^2 + 2xy + 5x^2 – 4xy + 7x
In this expression, the terms 3x^2, 5x^2, and 7x^2 are like terms since they have the same variable (x) raised to the same power (2). Similarly, the terms 2xy and -4xy are also like terms since they have the same variables (x and y).
To combine like terms, you can add or subtract their coefficients. The coefficients are the numbers multiplied by the variables. In the example:
3x^2 + 5x^2 + 7x^2 = (3 + 5 + 7)x^2 = 15x^2
2xy – 4xy = (2 – 4)xy = -2xy
So, the final simplified expression for 3x^2 + 2xy + 5x^2 – 4xy + 7x is:
15x^2 – 2xy + 7x
Remember that only like terms can be combined. Terms with different variables, different exponents, or different combinations of variables cannot be combined directly.
For example, you cannot combine terms like 3x^2 and 2xy because they have different variables (x and y) in addition to different exponents (2 and 1, respectively).
Overall, recognizing and combining like terms allows you to simplify expressions, solve equations, and make calculations more manageable in algebra.
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