$-10xy^2 - 12xy^2 = -22xy^2$ - Coaching Toolbox
Understanding the Equation: $-10xy^2 - 12xy^2 = -22xy^2$
Understanding the Equation: $-10xy^2 - 12xy^2 = -22xy^2$
Mathematics often presents equations that, at first glance, seem complex but reveal clear patterns once analyzed. One such equation is:
$$
-10xy^2 - 12xy^2 = -22xy^2
$$
Understanding the Context
In this article, we’ll break down this equation step-by-step, explain its structure, simplify it properly, and explore its implications for algebraic reasoning and solving similar expressions. Whether you’re a student, teacher, or math enthusiast, understanding this equation strengthens your foundational algebra skills.
Breaking Down the Equation
Start with the original expression:
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Key Insights
$$
-10xy^2 - 12xy^2 = -22xy^2
$$
Both terms on the left-hand side share the common factor $ -xy^2 $. Recognizing this common factor helps simplify and verify the equality.
Step 1: Combine Like Terms on the Left
We combine the coefficients of $ xy^2 $:
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$$
-10xy^2 - 12xy^2 = (-10 - 12)xy^2 = -22xy^2
$$
So the left side simplifies neatly to:
$$
-22xy^2
$$
Step 2: Rewrite the Full Equation After Simplification
Substituting back into the original equation:
$$
-22xy^2 = -22xy^2
$$
This shows both sides of the equation are identical.
