Question

Simplify each expression. $2\left(x^{2}+4 x-1\right)+3\left(2 x^{2}-2 x+2\right)$

   Simplify each expression.
$2\left(x^{2}+4 x-1\right)+3\left(2 x^{2}-2 x+2\right)$

Intermediate Algebra

Intermediate Algebra

Alan S. Tussy, R.… 5th Edition

Chapter 6, Problem 95

Instant Answer

Solved by Expert Alison Rodriguez

02/25/2023

Step 1

This gives us: \[2x^{2}+8x-2+6x^{2}-6x+6\] Show more…

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Simplify each expression. $2\left(x^{2}+4 x-1\right)+3\left(2 x^{2}-2 x+2\right)$

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Key Concepts

Combining Like Terms

Combining like terms is the process of simplifying expressions by merging terms that have identical variable parts. This technique is essential for reducing polynomials to their simplest form. It involves adding or subtracting coefficients of terms that have the same variables raised to the same powers, streamlining the expression for further manipulation or solving.

Polynomial Expressions

This concept involves working with expressions that consist of variables, coefficients, and exponents combined using addition, subtraction, and multiplication. Polynomial expressions are the foundation of algebra and require techniques such as expansion, simplification, and factoring to solve equations, analyze functions, or integrate in calculus.

Distributive Property

The distributive property is a fundamental algebraic principle that involves multiplying a single term across terms within parentheses. This property allows the multiplication of a constant or variable outside the parentheses with each term inside, enabling the expansion of expressions and simplifying complex polynomial equations.

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