Which expression is equivalent to 10x2y 25×2 – In the realm of algebra, the expression 10x^2y + 25x^2 presents a compelling exploration into the intricacies of factorization, simplification, and equivalent expressions. Embarking on this mathematical journey, we unravel the secrets of this expression, uncovering its hidden symmetries and practical applications.
Factorization, the process of breaking down an expression into its constituent parts, provides the foundation for our analysis. By carefully applying relevant formulas and techniques, we meticulously dissect 10x^2y + 25x^2, revealing the factors that contribute to its structure.
Factoring 10x^2y + 25x^2
To factor the expression 10x^2y + 25x^2, we can use the greatest common factor (GCF) method.
Step 1: Find the GCF of the coefficients 10 and 25. The GCF is 5.
Step 2: Find the GCF of the variables x^2 and y. The GCF is x^2.
Step 3: Factor out the GCF from the expression: 10x^2y + 25x^2 = 5x^2(2y + 5)
Simplification
To simplify the expression 10x^2y + 25x^2, we can combine like terms.
Step 1: Combine the terms with the same variables: 10x^2y + 25x^2 = 35x^2
Equivalent Expressions: Which Expression Is Equivalent To 10x2y 25×2
Equivalent expressions are expressions that have the same value for all values of the variables.
- 10x^2y + 25x^2 = 5x^2(2y + 5)
- 10x^2y + 25x^2 = 35x^2
Applications
The expression 10x^2y + 25x^2 can be used in various applications, such as:
- Calculating the area of a rectangle with sides of length x and y
- Modeling the volume of a rectangular prism with sides of length x, y, and z
Expert Answers
Is 10x^2y + 25x^2 always positive?
Yes, since both x^2 and y^2 are always non-negative, their sum 10x^2y + 25x^2 is also non-negative.
Can 10x^2y + 25x^2 be factored further?
No, 10x^2y + 25x^2 is already in its fully factored form. It cannot be broken down into simpler factors without introducing complex numbers.
