Find each product. [(4y-1)+z]2

Ch. R - Review of Basic Concepts

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

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 52

1장, 문제 52

Find each product. [(4y-1)+z]²

검증된 단계별 안내

Recognize that the expression is a square of a binomial: $[(4y - 1) + z]^2$. This can be treated as $(A + B)^2$ where $A = (4y - 1)$ and $B = z$.

Recall the formula for the square of a binomial: $(A + B)^2 = A^2 + 2AB + B^2$.

Calculate $A^2$ by squaring $(4y - 1)$: $(4y - 1)^2 = (4y)^2 - 2 \times 4y \times 1 + 1^2$.

Calculate \$2AB$ by multiplying $2 \times (4y - 1) \times z$.

Calculate $B^2$ by squaring $z$: $z^2$. Then, combine all parts to write the expanded expression: $A^2 + 2AB + B^2$.

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주요 개념

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

Binomial Expansion

Binomial expansion involves expressing the square of a sum or difference of two terms as a trinomial. For example, (a + b)^2 expands to a^2 + 2ab + b^2. This formula helps simplify expressions like [(4y - 1) + z]^2 by treating (4y - 1) as one term and z as the other.

Polynomial Operations

Polynomial operations include addition, subtraction, multiplication, and exponentiation of polynomial expressions. Understanding how to multiply and combine like terms is essential when expanding expressions such as [(4y - 1) + z]^2 to simplify the result correctly.

Like Terms and Simplification

Like terms are terms in a polynomial that have the same variables raised to the same powers. After expanding an expression, combining like terms simplifies the expression into its simplest form, making it easier to interpret and use in further calculations.