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🧮 Working with Expressions Lab

Check the laws of exponents,
then group up the like terms

Expressions with letters aren't hard once you know the rules. Try out the laws of exponents (adding and subtracting exponents), and simplifying a polynomial by grouping like terms — hands-on, right here.

An expression like x³, where a letter has an exponent attached, is called a monomial. An exponent is really just shorthand for "how many times something was multiplied," so multiplying the same letter together means adding the exponents, and dividing means subtracting them — because chaining together "x multiplied 3 times" and "x multiplied 2 times" ends up exactly the same as "x multiplied 5 times."

When simplifying a polynomial with several mixed terms, just group the like terms (terms whose letter and exponent match exactly) and add or subtract their coefficients. Just like subtracting 2 apples from 3 apples, you handle the x's with the x's and the plain numbers with the plain numbers.

Change the exponents with the sliders to see why the multiplication and division rules hold, and practice grouping scattered terms into like terms to simplify a polynomial.

Laws of exponents: multiplying two numbers with the same base adds the exponents (xm×xn=xm+n), and dividing subtracts them (xm÷xn=xm−n). That's because combining "x multiplied m times" with "x multiplied n times" ends up the same as "x multiplied (m+n) times."
x's exponent m3
x's exponent n2
Like terms are terms whose letter and exponent are exactly the same (e.g. 3x and −2x are like terms, but 3x and 3x² are not). Grouping scattered terms into like terms lets you simplify a polynomial into a much shorter form.
Problem 1
Press the group button and the simplified expression appears here