# Expand Algebraic Expressions Calculator

Use * to indicate multiplication between coefficients and variables. For example, write 4*x+5*x, instead of 4x+5x.

**Answer:**

**Examples:**

- To write \((2x+3)^2\), enter (2*x+3)^2.
- To write \((\frac{2}{3}x+\frac{4}{3})^2+2x\), enter (2/3*x+4/3)^2+2*x.
- To write \((\frac{2}{3x}+\frac{4}{3})^2+2x\), enter (2/(3*x)+4/3)^2+2*x.

This calculator allows you to obtain an expanded version of the algebraic expression entered. You can enter polynomials, rational expressions, exponentials, among others.

## How to use the calculator to expand algebraic expressions?

**Step 1:** Enter the algebraic expression in the corresponding input box. Use * to indicate multiplication between variables and coefficients. For example, enter 4*x or 3*x^2, instead of 4x or 3x^2.

**Step 2:** Click “Expand” to get the expanded version of the algebraic expression entered.

**Step 3:** The solution along with the algebraic expression will be displayed at the bottom.

## How to enter expressions in the calculator?

To enter algebraic expressions, we must use the * sign to indicate multiplication between variables and exponents. Also, we must use the ^ sign to indicate an exponent. For example,

- To write \((5x-2)^3\), enter (5*x-2)^2.
- To write \((\frac{1}{3}x+\frac{1}{3})^2+2x\), enter (1/3*x+1/3)^2+2*x.
- To write \((\frac{1}{3x}+\frac{1}{3})^2+2x\), enter (1/(3*x)+1/3)^2+2*x.

It is also important to use parentheses to correctly indicate operations. For example, by entering (5*x-2)^2, we indicate that the exponent is applied to the entire expression inside the parentheses. Also, by writing 1/(3*x) we indicate that the entire expression inside the parentheses is in the denominator of the fraction.

## How to expand algebraic expressions?

The expansion of algebraic expressions involves the removal of parentheses and other grouping signs. To eliminate these grouping signs, we often have to use the distributive property or apply the indicated exponent.

If we have an expression of the form (x+1)(2x+2), we can expand it using the distributive property and multiply each term in the first parentheses by each term in the second parentheses.

If we have an expression of the form \((x+2)^3\), we can expand it using the binomial theorem. In this way, we will obtain the coefficients and the exponents of each term of the expanded version.

## Why expand algebraic expressions?

By expanding algebraic expressions, we can obtain a simpler version of the expression. Since the expression will be fully expanded, it is also possible to find all like terms to combine them to get the simplest possible version.

Often, expanded versions can make it easier to perform some operations, such as finding derivatives.

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