Find each product. 2b3(b2−$$4b+3)2b^3$(b^2-4b+3)$$

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 34

1장, 문제 34

Find each product. $2 b^{3} (b^{2} - 4 b + 3)$

검증된 단계별 안내

Identify the expression to be multiplied: $2b^3(b^2 - 4b + 3)$.

Apply the distributive property by multiplying \$2b^3$ with each term inside the parentheses separately.

Multiply \$2b^3$ by the first term: $b^2$. This gives $2b^3 \times b^2 = 2b^{3+2} = 2b^5$.

Multiply \$2b^3$ by the second term: $-4b$. This gives $2b^3 \times (-4b) = -8b^{3+1} = -8b^4$.

Multiply \$2b^3$ by the third term: $3$. This gives $2b^3 \times 3 = 6b^3$. Then, write the product as the sum of these terms: $2b^5 - 8b^4 + 6b^3$.

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.

Polynomial Multiplication

Polynomial multiplication involves distributing each term in one polynomial to every term in the other polynomial. This process requires applying the distributive property to combine like terms and simplify the expression.

Exponent Rules

When multiplying terms with the same base, add their exponents. For example, b^3 multiplied by b^2 equals b^(3+2) = b^5. Understanding this rule is essential for correctly simplifying powers during multiplication.

Distributive Property

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term inside a parenthesis, which is crucial for expanding expressions like 2b^3(b^2 - 4b + 3).

Find each product. 2b3(b2−4b+3)2b^3(b^2-4b+3)