📚 Practice With Worksheets
Continue practicing combining like terms, matching equivalent expressions, and writing equivalent perimeter expressions.
▶️ Learn With Videos
Review how distributing, factoring, combining like terms, and writing perimeter expressions create equivalent algebraic forms.
🛠️ How to Use This Tool
Choose Whole Numbers, Fractions, Decimals, or a combination of number types. Turn on Negatives to include positive and negative values within the selected modes.
Use Distribute, Combine Like Terms, or Factor Out GCF to create a different form of the starting expression without changing its value. Reset or undo a move whenever you want to compare forms again.
On the right, select every expression that is equivalent to the starting expression, then check your choices. The feedback marks each correct selection, missed equivalent form, incorrect selection, and correctly rejected expression.
🧠 Things to Notice
Equivalent expressions may look different because terms can be distributed, combined, reordered, factored, or written in another number form.
When fractions and decimals are active together, the same coefficient may appear as a fraction, mixed number, or decimal. Compare values carefully instead of relying only on appearance.
A negative sign can change the meaning of an entire term or group. Check whether the sign is being distributed correctly and whether like terms truly have matching variable parts.
📘 Vocabulary
Expression: A mathematical phrase containing numbers, variables, and operations.
Term: A number, variable, or product separated from other terms by addition or subtraction.
Like Terms: Terms with identical variable parts and exponents.
Equivalent Expressions: Expressions that have the same value for every value of the variable.
Distributive Property: Multiplying a factor by every term inside parentheses.
Combining Like Terms: Adding or subtracting the coefficients of terms with matching variable parts.
Factor: A number or expression multiplied by another number or expression to form a product.
Factoring: Rewriting an expression as a product of factors.
Greatest Common Factor (GCF): The greatest positive factor shared by all terms in an expression.
Coefficient: The numerical factor multiplied by a variable.
📐 Creating Equivalent Expressions
The distributive property creates an equivalent expression by multiplying the outside factor by every term inside the parentheses.
\(a(b+c)=ab+ac\)
Like terms can be combined because they represent the same variable quantity. Their coefficients are added or subtracted while the variable part stays unchanged.
\(ax+bx=(a+b)x\)
Factoring reverses distribution. When factoring out the GCF, divide every term by the same greatest positive common factor and place the quotients inside parentheses.
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