Find each product : (4x+5)(4x-5)

검증된 단계별 안내

Recognize that the expression (4x + 5)(4x - 5) 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: \(\\(a + b)(a - b) = a^2 - b^2\\)\).

Identify \(a = 4x\) and \(b = 5\) in the given expression.

Apply the formula by squaring each term: calculate \(a^2 = (4x)^2\) and \(b^2 = 5^2\).

Write the product as \(a^2 - b^2 = (4x)^2 - 5^2\), which simplifies to \(16x^2 - 25\).

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주요 개념

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Distributive Property

The distributive property allows you to multiply each term inside one parenthesis by each term inside the other. It is essential for expanding expressions like (a + b)(c + d) by multiplying each pair of terms and then combining like terms.

Difference of Squares

The difference of squares is a special product formula: (a + b)(a - b) = a² - b². Recognizing this pattern simplifies multiplication when two binomials have the same terms but opposite signs between them.

Combining Like Terms

After expanding an expression, combining like terms means adding or subtracting terms with the same variable and exponent. This step simplifies the expression to its simplest form for easier interpretation or further operations.