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

Verified step by step guidance

1. Recognize that the expression \((4x+5)(4x-5)\) is a difference of squares.
2. Recall the formula for the difference of squares: \((a+b)(a-b) = a^2 - b^2\).
3. Identify \(a = 4x\) and \(b = 5\) in the expression.
4. Apply the difference of squares formula: \((4x)^2 - (5)^2\).
5. Simplify the expression: \(16x^2 - 25\).

Key Concepts

Factoring and the Difference of Squares

The expression (4x+5)(4x-5) is an example of the difference of squares, which follows the formula a^2 - b^2 = (a+b)(a-b). Here, a is 4x and b is 5. Recognizing this pattern allows for quick simplification and understanding of how to multiply these binomials.

Binomial Multiplication

Binomial multiplication involves multiplying two binomials, which can be done using the distributive property or the FOIL method (First, Outside, Inside, Last). This method ensures that each term in the first binomial is multiplied by each term in the second, leading to a complete product.

Combining Like Terms

After multiplying the binomials, the resulting expression may contain like terms, which are terms that have the same variable raised to the same power. Combining these terms simplifies the expression, making it easier to interpret and work with in further calculations.