Which expression is equivalent to 3x-5y x 2y – Embark on a mathematical odyssey as we delve into the captivating world of algebraic expressions. At the forefront of our exploration lies the enigmatic query: which expressions possess the same value as 3x-5y x 2y? Prepare to unravel the secrets of equivalent expressions, uncovering their significance and unlocking their practical applications.
Through a journey of simplification, substitution, and exploration, we shall illuminate the intricate tapestry of algebraic equivalency, empowering you with a profound understanding of this fundamental mathematical concept.
Understanding the Expression
The expression ‘3x-5y x 2y’ represents a mathematical operation involving two variables, x and y. This expression is significant because it demonstrates the application of basic arithmetic operations, namely multiplication and subtraction, within a single mathematical statement.
The expression ‘3x’ represents the product of the coefficient 3 and the variable x. Similarly, ‘5y’ represents the product of the coefficient 5 and the variable y. The ‘x’ term in ‘3x-5y’ and the ‘y’ term in ‘2y’ indicate that the expression is a polynomial of degree 1.
To illustrate the meaning of the expression, consider the following examples:
- If x = 2 and y = 3, then ‘3x-5y x 2y’ becomes 3(2) – 5(3) x 2(3) = 6 – 30 x 6 = -168.
- If x = -1 and y = 4, then ‘3x-5y x 2y’ becomes 3(-1) – 5(4) x 2(4) = -3 – 40 x 8 = -323.
Simplifying the Expression
To simplify the expression ‘3x-5y x 2y’, we apply the rules of multiplication and subtraction:
- Multiply the terms ‘5y’ and ‘2y’ first: 5y x 2y = 10y^2.
- Substitute the result from step 1 into the original expression: 3x
10y^2.
Therefore, the simplified expression is 3x – 10y^2.
Equivalent Expressions: Which Expression Is Equivalent To 3x-5y X 2y
Expressions that have the same value for all values of the variables involved are called equivalent expressions. To find equivalent expressions for ‘3x-5y x 2y’, we can use the following methods:
- Factoring:We can factor out a common factor from the expression to obtain an equivalent expression. For example, 3x – 10y^2 = x(3 – 10y^2).
- Substitution:We can substitute one expression for another that is equivalent to it. For example, if we let u = 3x – 5y, then ‘3x-5y x 2y’ can be written as u x 2y.
- Algebraic manipulation:We can use algebraic operations, such as adding or subtracting the same term on both sides of the equation, to obtain an equivalent expression. For example, 3x – 10y^2 + 10y^2 = 3x.
Applications of the Expression
The expression ‘3x-5y x 2y’ can be applied in various fields, including:
- Physics:In kinematics, the expression can be used to calculate the acceleration of an object moving in a straight line with constant acceleration.
- Economics:In microeconomics, the expression can be used to represent the total cost of production, where x represents the quantity produced and y represents the variable cost per unit.
- Computer science:In computer graphics, the expression can be used to calculate the area of a triangle, where x and y represent the coordinates of the triangle’s vertices.
Essential Questionnaire
What is the significance of equivalent expressions?
Equivalent expressions provide multiple representations of the same mathematical value, offering flexibility in problem-solving and enhancing our understanding of algebraic relationships.
How can we find equivalent expressions?
Techniques for finding equivalent expressions include simplifying, substituting equivalent expressions, and applying algebraic properties such as the distributive property.
What are some real-world applications of equivalent expressions?
Equivalent expressions find practical applications in various fields, including physics, engineering, and economics, where they simplify complex calculations and facilitate problem-solving.
