Combining like terms simplifying expressions and finding equivalent expressions

Combina términos similares para simplificar expresiones y encontrar expresiones equivalentes. Simplifica ecuaciones algebraicas y hace más fácil su resolución. Examples incluidos. Carefully combine like terms to simplify algebraic expressions and mak

March 9, 2023· 2 min read
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Combining like terms

Combining like terms is an important skill to have when solving algebraic equations. To combine like terms, you must first identify which terms are alike. Like terms are terms that contain the same variables raised to the same power. For example, 4x and 2x are like terms because they both have the variable x, and the power of x is the same in both terms.

Once you have identified the like terms, you can combine them by adding or subtracting the coefficients. The coefficient is the number that is multiplied by the variable. In the example of 4x and 2x, the coefficients are 4 and 2, respectively. To combine the terms, add the coefficients together, which in this case would result in 6. So, 4x + 2x = 6x.

Another example of combining like terms is 3x2 + 5x2. In this case, the variables are the same (x) and the powers are the same (2), so these are like terms. To combine them, add the coefficients together, which in this case would be 3 + 5 = 8. So, 3$\cdot$2 + 5$\cdot$2 = 8$\cdot$2.

Combining like terms is a key skill to have when solving algebraic equations. It allows you to simplify equations and make them easier to solve. By identifying which terms are alike and adding or subtracting the coefficients, you can combine like terms and make equations more manageable.

more examples

$4(x+3)-5=4x+12-5$

$2(x+3)\cdot x=2x+6$

Simplifying expressions

Simplifying expressions is a key part of algebra. It involves taking an expression and reducing it to its simplest form. This can involve combining like terms, factoring polynomials, or using the distributive property. It is important to simplify expressions because it helps to make them easier to work with and understand.

One way to simplify an expression is to combine like terms. This involves looking for terms that have the same variable and coefficient and then combining them into one term. For example, if you have 3x + 5x, you can combine them to get 8x. This simplifies the expression and makes it easier to work with.

Another way to simplify an expression is to factor polynomials. This involves looking for common factors in the terms of the polynomial and then factoring them out. For example, if you have 3x2 + 6x, you can factor out 3x to get 3x(x + 2). This simplifies the expression and makes it easier to work with.

The last way to simplify an expression is to use the distributive property. This involves distributing the terms of the expression to make it easier to work with. For example, if you have 3(x + 2), you can use the distributive property to get 3x + 6. This simplifies the expression and makes it easier to work with.

Examples

$16-8+4-1=8+3=11$

$7+9-10+3=15-13=2$

$17+8-20-2=15-18=3$

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