Textbook Question
In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms.(5x + 3)(5x − 3)
772
views
0. Review of Algebra
Polynomials Intro
1:42 minutesProblem 77
Textbook Question
Find each product : (4x+5)(4x-5)
Verified step by step guidance1
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$.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
Recommended video:
Guided course
04:15
Multiply Polynomials Using the Distributive Property
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.
Recommended video:
06:24Solving Quadratic Equations by Completing the Square
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.
Recommended video:
5:22Combinations
Related Videos
Related Practice