Combine like terms accurately across powers, fractions, decimals, and multivariable expressions.
This test has 20 questions
A shorter expression is useful only if it stays equivalent to the original. That makes simplification different from solving an equation: there may be no unknown value to find. Instead, you remove unnecessary structure, distribute factors, combine like terms, and preserve every sign and exponent.
The exact expression may vary, but this workflow handles most linear and polynomial simplification tasks cleanly.
Two terms are like terms only when every variable has the same exponent in both terms.
The inner subtraction is the important step. Subtracting (x − 4) means subtracting x and subtracting −4, so the constant becomes +4. Once the inner grouping is correct, the outer distribution is routine.
If the variable parts match, combine the fractional coefficients exactly as ordinary fractions.
Do not begin combining until the second group has been rewritten with changed signs.
The last term becomes +6 because subtracting −6 is addition.
Substitution does not prove two expressions are equivalent for every value, but one mismatched test value proves that they are not equivalent.
At x = 4, the original gives 3(6) − 4 = 14 and the simplified form gives 8 + 6 = 14. This is a useful check after the algebraic simplification.
The outside factor multiplies every term inside the parentheses.
The variable parts x and x² are different, so these are unlike terms.
Multiplying the entire group by −1 changes both signs.
Addition combines coefficients. Exponents are not added when terms are added.
This is more useful than memorizing one corrected expression, because the same structural mistake can appear in many different forms.