step 1 In this problem, we're being asked to expand the given expression. So we have the binomial x min

Question

$\left(x-x^{2}\right)\left(x+x^{2}\right)$

Name: Problem 16, Chapter 0: Finite Mathematics and Applied Calculus
Uploaded: 2021-09-22T21:38:41-08:00
Duration: 1 min 6 s
Channel: Julie Silva
Description: (x-x^2)(x+x^2)

   $\left(x-x^{2}\right)\left(x+x^{2}\right)$

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 5th Edition

Chapter 0, Problem 16

Instant Answer

Solved by Expert Julie Silva

09/22/2021

Step 1

We can see that this is in the form of $(a-b)(a+b)$, where $a=x$ and $b=x^2$. Show more…

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$\left(x-x^{2}\right)\left(x+x^{2}\right)$

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Key Concepts

Exponent Rules

These rules govern how powers are combined during operations such as multiplication. When multiplying terms with the same base, the exponents are added together. This is crucial in simplifying expressions where variables are raised to powers.

Difference of Squares

A common algebraic factoring pattern where an expression in the form a² - b² can be rewritten as (a - b)(a + b). Recognizing this pattern allows for quick simplification or factorization of expressions, even when the terms involve variables raised to different powers.

Distributive Property

This fundamental property of algebra allows for the multiplication of a term by a sum or difference, ensuring that each term in one expression is multiplied by every term in the other. It is key when expanding products of binomials, making the process systematic and reliable.

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