Question

Multiply. $$ (x 2-x+1)(x 2+2 x+1) $$

Name: Problem 61, Chapter 5: Elementary Algebra
Uploaded: 2022-02-02T17:44:54-08:00
Duration: 53 s
Channel: James Kiss
Description: Multiply. (x 2-x+1)(x 2+2 x+1)

   Multiply.
$$
(x 2-x+1)(x 2+2 x+1)
$$

Elementary Algebra

John Redden 1st Edition

Chapter 5, Problem 61

Instant Answer

Solved by Expert James Kiss

02/02/2022

Step 1

This gives us: $$ x^2 \cdot x^2 + x^2 \cdot 2x + x^2 \cdot 1 = x^4 + 2x^3 + x^2 $$ Show more…

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Multiply. $$ (x 2-x+1)(x 2+2 x+1) $$

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Key Concepts

Combining Like Terms

After multiplying the terms of the polynomials, the next crucial step is to combine like terms. This involves adding coefficients of terms that have the same degree or variable components, which simplifies the resulting expression into its standard polynomial form.

Polynomial Multiplication

This concept involves multiplying two polynomials together to form a new, expanded polynomial. It requires applying the distributive property to ensure that every term in the first polynomial is multiplied by every term in the second polynomial, generating all possible products before combining them.

Distributive Property

The distributive property is a fundamental algebraic principle used in polynomial multiplication. It states that a(b + c) equals ab + ac, and when applied to polynomials, it ensures that each term in one polynomial multiplies every term in the other. This is essential for expanding and simplifying expressions involving polynomials.

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