Find each product. [(2p-3)+q]2

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 51

1장, 문제 51

Find each product. [(2p-3)+q]²

검증된 단계별 안내

Recognize that the expression is a square of a binomial: \([(2p - 3) + q]^2\). This can be treated as \((a + b)^2\) where \(a = (2p - 3)\) and \(b = q\).

Recall the formula for the square of a binomial: \((a + b)^2 = a^2 + 2ab + b^2\).

Calculate each term separately: first, find \(a^2 = (2p - 3)^2\) by expanding it using the formula \((x - y)^2 = x^2 - 2xy + y^2\).

Next, find the middle term \(2ab = 2 imes (2p - 3) imes q\) by multiplying the terms carefully.

Finally, find \(b^2 = q^2\). Then, combine all three results to write the expanded form of the original expression.

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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 method helps simplify expressions like [(2p - 3) + q]^2 by applying the formula directly.

Combining Like Terms

After expanding an expression, combining like terms means adding or subtracting terms that have the same variable raised to the same power. This step simplifies the expression into its simplest form, making it easier to interpret or use in further calculations.

Distributive Property

The distributive property states that a(b + c) = ab + ac. It is used to multiply each term inside the parentheses by the term outside or by each other during expansion. This property is fundamental when expanding expressions like [(2p - 3) + q]^2.