The Equivalent expressions calculator uses advanced algorithms to simplify and transform expressions into equivalent forms, providing you with step-by-step explanations along the way. This makes it easy for you to understand the process and learn how to solve similar problems in the future.
To use the Equivalent expressions calculator you just have to enter an algebraic expression and press the “Calculate” button, and you will automatically obtain the equivalent expression explained step by step.
Equivalent expressions are algebraic expressions (two or more) that represent the same quantity. These may have a different structure, but their numerical value will be the same.
For example, in the following equality, both sides represent the same quantity:
12xy·(1/x+y) = 12y+12xy2
To find equivalent algebraic expressions, you can use several techniques. Here are some of them:
Simplify the expressions using the order of operations (PEMDAS): Evaluate any expressions inside parentheses, then perform any multiplication or division from left to right, and finally perform any addition or subtraction from left to right. This can help you simplify the expressions and identify any common terms.
Use the distributive property: The distributive property states that a(b + c) = ab + ac. You can use this property to expand or simplify expressions. For example, 2(x + y) can be expanded as 2x + 2y.
Combine like terms: If you have expressions with similar terms, you can combine them. Like terms have the same variable and exponent. For example, 2x + 3x can be combined as 5x.
Factor expressions: If you have expressions that have common factors, you can factor them out. For example, x^2 + 3x can be factored as x(x + 3).
Use algebraic identities: There are several algebraic identities that you can use to simplify or transform expressions. For example, (a + b)2 = a2 + 2ab + b2 is an identity that can be used to expand expressions. Similarly, (a + b)(a – b) = a2 – b2 is an identity that can be used to factor expressions.
Substitute variables: If you have expressions with variables, you can substitute them with equivalent expressions. For example, if you have 2x + 3y, you can substitute y = 2x + 1 to get 2x + 3(2x + 1)