Perform the indicated operations and simplify each expression. 2(x-1)(2 x+2)^3[4(x-1)+(2 x+2)]

Name: Problem 123, Chapter 1: Applied Calculus for the MLSS A Brief Approach
Uploaded: 2021-05-06T21:49:49-08:00
Duration: 1 min 15 s
Channel: Tyler Moulton
Description: Perform the indicated operations and simplify each expression. 2(x-1)(2 x+2)^3[4(x-1)+(2 x+2)]

step 1 We want to simplify the expression 2 times x minus 1 times 2x plus 2 squared times the quantity

Perform the indicated operations and simplify each...

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Key Concepts

Combining Like Terms

Combining like terms involves adding or subtracting terms in an algebraic expression that have identical variable parts. This process consolidates the expression by reducing the number of terms and is a key step in achieving a simplified final form.

Exponentiation Rules

Exponentiation rules provide guidelines for raising terms to a power, particularly when the term is a product or a sum. Understanding these rules is crucial when simplifying expressions that include binomials raised to a power or other exponential forms.

Algebraic Expression Simplification

Simplification of algebraic expressions involves reducing expressions to their simplest form by performing operations such as expansion, factoring, and combining like terms. This process ensures that the expression is easier to interpret and work with in subsequent calculations or problem-solving steps.

Distributive Property

The distributive property allows you to multiply a factor across a sum or difference inside parentheses. It is essential in both expanding products of binomials or larger polynomials and simplifying expressions where multiple terms are involved.

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