Question

Simplify.Add $6 x^{2}+12 x y$ and $-2 x^{2}+4 x y+3 y$

Name: Problem 56, Chapter 5: Intermediate Algebra for College Students
Uploaded: 2020-05-12T00:45:14-08:00
Duration: 1 min 31 s
Channel: Manuel Andrade-Panek
Description: Simplify.Add 6 x^2+12 x y and -2 x^2+4 x y+3 y

   Simplify.Add $6 x^{2}+12 x y$ and $-2 x^{2}+4 x y+3 y$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 5, Problem 56

Instant Answer

Solved by Expert Manuel Andrade-Panek

05/12/2020

Step 1

In the first expression, we have $6x^2$ and $12xy$. In the second expression, we have $-2x^2$, $4xy$, and $3y$. The like terms are $6x^2$ and $-2x^2$, and $12xy$ and $4xy$. Show more…

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Simplify.Add $6 x^{2}+12 x y$ and $-2 x^{2}+4 x y+3 y$

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Key Concepts

Polynomial Addition

Polynomial addition involves summing two or more polynomials by adding the coefficients of corresponding terms. It requires aligning terms that have the exact same variables and exponents. This operation is fundamental in algebra and is based on the commutative and associative properties of addition, which allow terms to be rearranged and grouped without changing the sum.

Like Terms

Like terms are terms in an algebraic expression that have the same variable components raised to the same powers. Identifying and combining like terms simplifies expressions because only the coefficients are altered during addition or subtraction. This process is crucial for consolidating expressions into their simplest form and is a key step in solving polynomial equations.

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