Simplifying Algebraic Expressions: A Step-by-Step Guide with 15Xy-13+4X+3Y+Xy+21

15xy + 4x + 3y + 22

Simplify The Algebraic Expression 15Xy-13+4X+3Y+Xy+21

This algebraic expression is an important tool to simplify complex mathematical equations. By evaluating this equation, we can derive a simplified version which allows for further calculations to be made with greater ease. To do this, we must examine the individual components of the expression and combine like terms. The expression consists of five parts: 15Xy-13+, 4X+3Y, Xy+21.

Lets start from the left: 15Xy-13+. This is a monomial term as it involves only one variable; in this case X, multiplied by another single factor; in this case Y; and finally a constant -13. Now let’s look at the next element – 4X+. Here we have a binary term involving X alone, multiplied by the constant 4. Thirdly, we have 3Y+. This consists of a variable Y and the constant 3.

The fourth component is comprised of two terms: Xy+21. As both these terms involve two variables – X and Y – these can be considered as like monomials; meaning they will add together upon evaluation of this equation. Finally, we have 21, a constant number with no variables attached.

Overall, combining all like terms in this equation gives us 19Xy + 4x + 3Y + 21 . This simplified form provides us with an easier form to evaluate further calculations if need be or to plug into other equations greater ease.

Introduction

Algebraic expressions are equations with numbers, variables, and operations. Simplifying is the process of combining like terms in an expression and reducing it to its simplest form. In this article, we will be looking at how to simplify the algebraic expression 15xy-13+4x+3y+xy+21.

What is an Algebraic Expression?

An algebraic expression is a combination of numbers, variables, and operations (like addition or multiplication). A variable is a letter that can represent any number. An example of an algebraic expression is 5x + 3y. In this expression, x and y are variables and 5 and 3 are numbers. The operation between them is addition.

Simplifying Algebraic Expressions

Simplifying an algebraic expression means that you combine like terms and reduce the expression to its simplest form. Like terms are terms that have the same variable(s). For example, in the expression 7x + 4x, the two terms have the same variable (x), so they can be combined into one term (11x).

Simplifying The Algebraic Expression 15Xy-13+4X+3Y+Xy+21

Let us now look at how to simplify this particular algebraic expression: 15xy-13+4x+3y+xy+21.

The first step in simplifying this equation is to combine like terms. In this case, there are two terms with xy: 15xy and xy. We can combine these two terms into one term (16xy). Now our equation looks like this: 16xy-13 + 4x + 3y + 21.
The next step is to combine all of the x terms together and all of the y terms together; this will give us our final simplified equation: 16xy – 13 + 7x + 24y.

Conclusion

In conclusion, we have gone through how to simplify an algebraic expression by combining like terms and reducing it to its simplest form. We have taken a look at how to do this for the equation 15xy-13 + 4x + 3y + xy + 21 by combining like terms first (16xy) and then further simplifying it (16xy – 13 + 7x + 24y).

Introduction

In mathematics, an algebraic expression is an expression that contains one or more terms combined through the operations of addition, subtraction, multiplication and division. Simplifying an algebraic expression involves combining like terms and removing unnecessary operations. In this article, we will look at the process of simplifying the algebraic expression 15Xy-13+4X+3Y+Xy+21.

Combining Like Terms

The first step in simplifying any algebraic expression is to combine like terms. Like terms are terms with the same variable raised to the same power. In this example, we have two like terms: Xy and Xy. These can be combined by adding the coefficients (the numbers which come before each term): 15Xy + Xy = 16Xy.

The other like term we have is 4X + X = 5X. We now have two separate expressions which can be combined to form one expression: 16Xy + 5X.

Subtracting

The next step in simplifying this expression is to subtract 13 from it: 16Xy + 5X – 13 = 16Xy + 5X – 13. Subtracting 13 from both sides of the equation yields 16Xy + 5x – 13 = 0.

Solving For X

We now need to solve for X in order to simplify this equation further. To do so, we will use the quadratic formula: x = (-b b-4ac)/2a where a = coefficient of x (in our case 0), b = coefficient of x (in our case 5), and c = constant (in our case -13). Substituting these values into the formula yields x = (-5 (25+52))/0 or x = (-5 77)/0 which simplifies to x = -5 77 or x 2 or -7.

Substituting Values Into Equation

Now that we know what value of x will simplify our equation, we can substitute it into our original equation: 16xy + 5x – 13 with x= 2 yields 32xy + 10 – 13 or 32xy – 3 and with x=-7 yields 112xy-70-13 or 112xy-83 . We can now combine these two equations by adding them together: 32xy-3 + 112xy-83 = 144xy-86 . This is our final simplified equation!

FAQ & Answers

Q: What is the algebraic expression?
A: The algebraic expression is 15Xy-13+4X+3Y+Xy+21.

Q: How can I simplify this expression?
A: To simplify this expression, you can combine like terms by adding the coefficients and multiplying the variables. This will result in 19Xy + 4X + 3Y + 21.

Q: What are like terms?
A: Like terms are terms that have the same variable raised to the same power or exponent. For example, 5x and 3x are like terms because they both have the variable x raised to the first power (x1).

Q: Is there a shortcut for simplifying expressions with multiple like terms?
A: Yes, there is a shortcut for simplifying expressions with multiple like terms. You can combine like terms by adding up their coefficients and multiplying their variables. For example, if you have 3x + 5x + 8x, you can add up the coefficients (3 + 5 + 8 = 16) and multiply them with x (16x). This will give you 16x as your simplified expression.

Q: How do I know if two algebraic expressions are equal?
A: To determine if two algebraic expressions are equal, you need to solve each of them separately and compare their values. If both expressions have the same value when solved then they are equal.

The simplified algebraic expression is: 19Xy + 4X + 3Y + 22. This expression can be simplified further by combining like terms, such as combining the X terms and Y terms, but this is the simplest form of the given expression.