Find each product. (y+2)3

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 57

1장, 문제 57

Find each product. (y+2)³

검증된 단계별 안내

Recognize that the expression \( (y+2)^3 \) represents a binomial raised to the third power, which means \( (y+2) \times (y+2) \times (y+2) \).

Use the binomial expansion formula for cubes: \( (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 \). Here, \( a = y \) and \( b = 2 \).

Calculate each term separately: \( a^3 = y^3 \), \( 3a^2b = 3 \times y^2 \times 2 \), \( 3ab^2 = 3 \times y \times 2^2 \), and \( b^3 = 2^3 \).

Write the expanded form by combining all the terms: \( y^3 + 3y^2 \times 2 + 3y \times 4 + 8 \).

Simplify the coefficients in each term to get the final expanded expression.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Binomial Expansion

Binomial expansion is the process of expanding expressions raised to a power, such as (a + b)^n, into a sum of terms involving coefficients, powers of a, and powers of b. It allows us to write the expression as a polynomial without directly multiplying multiple times.

Binomial Theorem and Coefficients

The Binomial Theorem provides a formula to expand (a + b)^n using binomial coefficients, which are found using combinations (n choose k). These coefficients determine the weight of each term in the expansion and can be found using Pascal's Triangle or the formula n!/(k!(n-k)!).

Polynomial Multiplication

Polynomial multiplication involves multiplying each term in one polynomial by every term in another and then combining like terms. For powers like (y + 2)^3, this means multiplying (y + 2) by itself three times and simplifying the resulting expression.