Find each product. (4x2-5y)(4x2+5y)

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 45

1장, 문제 45

Find each product. (4x²-5y)(4x²+5y)

검증된 단계별 안내

Identify the expression to be multiplied: \((4x^2 - 5y)(4x^2 + 5y)\).

Recognize that this is a product of two binomials in the form \((a - b)(a + b)\), which is a difference of squares pattern.

Recall the difference of squares formula: \((a - b)(a + b) = a^2 - b^2\).

Apply the formula by letting \(a = 4x^2\) and \(b = 5y\), so the product becomes \((4x^2)^2 - (5y)^2\).

Square each term separately: \((4x^2)^2 = 16x^4\) and \((5y)^2 = 25y^2\), then write the final expression as \(16x^4 - 25y^2\).

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주요 개념

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

Polynomial Multiplication

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

Difference of Squares

The difference of squares is a special product formula: (a - b)(a + b) = a^2 - b^2. Recognizing this pattern allows for quick multiplication and simplification of expressions that fit this form.

Combining Like Terms

After multiplying polynomials, like terms (terms with the same variables and exponents) must be combined by adding or subtracting their coefficients to simplify the final expression.