1Cademy - Simplifying $$c^2 + 7d^2

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Procedure for Combining Like Terms

Example

Simplifying $c^2 + 7d^2 - 6c^2$

Simplify the expression containing three monomials:

$c^2 + 7d^2 - 6c^2$

Identify the like terms: $c^2$ and $-6c^2$ are like terms because both contain the variable $c$ raised to the second power. The term $7d^2$ involves a different variable ( $d$ ), so it is not a like term with either of the $c^2$ -terms. Combine only the like terms by subtracting the coefficients: $1 - 6 = -5$ :

$c^2 + 7d^2 - 6c^2 = -5c^2 + 7d^2$

This example demonstrates that when an expression contains monomials with different variables, only those sharing the same variable and exponent can be combined. The unlike term $7d^2$ remains as is in the simplified result.