Which of the following is a like term of 7xy?

Unveiling the Secrets of Algebraic Expressions

In the realm of algebra, like terms reign supreme as expressions that share the same variables raised to the same powers. Navigating this mathematical landscape requires a keen eye for similarities, allowing us to group and combine like terms with ease. Join us on this illuminating journey as we embark on a quest to identify the kindred spirit of the enigmatic 7xy.

Solved Simplify and collect like terms: 9x−[4y−3(x−y)] A) | Chegg.com

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Like Terms: A Symphony of Similarities

Imagine a grand orchestral performance where musicians harmonize their instruments, blending their melodies into a cohesive symphony. In algebra, like terms play a similar role, uniting variables and powers in a harmonious ensemble. They share the same “building blocks,” denoted by the variables and their exponents. This commonality empowers us to combine like terms, amplifying their power and simplifying our algebraic expressions.

A Tale of Two Like Terms

Amidst the vast expanse of algebraic expressions, a special connection emerges between 7xy and 3xy. Like estranged siblings, they share a familial bond through the variable xy. Both terms possess the same two components, with x elevated to the first power and y mirroring this elevation. This shared lineage renders them like terms, destined to unite in algebraic harmony.

Distant Relatives: Unlike Terms

Venture beyond the realm of like terms, and we encounter distant relatives known as unlike terms. These mathematical entities may share a common variable, but their powers diverge, creating a barrier to their unification. Consider the expression 5x²y and 7xy. While they share the variable xy, the differing exponents of x (2 and 1, respectively) prohibit them from joining forces as like terms.

Solved If [2xy-7]=[2-56-7], then x= and y=If | Chegg.com

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The Art of Combining Like Terms

Unveiling the secrets of combining like terms is akin to conducting a symphony of algebraic expressions. Simply add or subtract the coefficients (the numbers accompanying the variables) while preserving the shared variables and powers. Witness how the coefficients of 7xy and 3xy merge, creating a new melodic term, 10xy:

7xy + 3xy = 10xy

Embracing Algebraic Harmony

Mastering the art of identifying and combining like terms transcends mere academic pursuits. This powerful technique orchestrates complex expressions into simplified masterpieces, unlocking the hidden beauty within algebraic equations. Let us embrace the harmony of like terms, transforming the symphony of algebra into a captivating masterpiece of mathematical elegance.