Question

Find each product. $$ -\frac{1}{100}(10 x+10)(10 x-10) $$

   Find each product.
$$
-\frac{1}{100}(10 x+10)(10 x-10)
$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Margaret L. Lial,… 7th Edition

Chapter 4, Problem 51

Instant Answer

Solved by Expert Yujie Wang

02/12/2022

Step 1

This gives us: $$ -\frac{1}{100}(10(x+1))(10(x-1)) $$ Show more…

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Find each product. $$ -\frac{1}{100}(10 x+10)(10 x-10) $$

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Key Concepts

Difference of Squares Identity

This key concept involves recognizing that any product of the form (a + b)(a ? b) simplifies to a^2 ? b^2. It serves as a shortcut in multiplying binomial expressions and reduces the need for term-by-term distribution. This identity is widely used in algebra to simplify expressions and solve equations efficiently.

Factoring Out Common Factors

Factoring out common factors is the process of identifying and removing a common multiplicative element from terms in an expression. This can simplify the multiplication and reduce complexity by canceling factors, especially when dealing with coefficients or variables shared by all terms, which is a common technique in algebraic manipulation.

Scalar Multiplication and Simplification

Scalar multiplication involves multiplying an entire expression by a constant factor. Simplification takes place by applying arithmetic operations along with factoring techniques, especially when a constant coefficient can cancel with a common factor in the product. This is crucial in reducing complex expressions to their simplest form in algebra.

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