Textbook Question
Multiply: (2x−5)(x²−3x−6). (Section 5.2, Example 3)
1035
views
0. Review of Algebra
Polynomials Intro
2:07 minutesProblem 87
Textbook Question
Find each product. (7x+4y)(7x-4y)
Verified step by step guidance1
Recognize that the given expression (7x+4y)(7x-4y) is a product of two binomials in the form (a+b)(a-b), which is a difference of squares formula.
Recall the difference of squares formula: (a+b)(a-b) = a² - b².
Identify the terms in the binomials: a = 7x and b = 4y.
Substitute the identified terms into the formula: a² - b² becomes (7x)² - (4y)².
Simplify each squared term: (7x)² = 49x² and (4y)² = 16y², so the expression simplifies to 49x² - 16y².
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Binomial Multiplication
Binomial multiplication involves multiplying two binomials, which are algebraic expressions containing two terms. The process typically uses the distributive property, often summarized by the acronym FOIL (First, Outside, Inside, Last) to ensure all combinations of terms are multiplied. For example, in the expression (a + b)(c + d), each term in the first binomial is multiplied by each term in the second.
Recommended video:
03:42
Finding Zeros & Their Multiplicity
Difference of Squares
The difference of squares is a specific algebraic identity that states that the product of two conjugates, such as (a + b)(a - b), equals a² - b². This identity simplifies the multiplication of binomials where one is the negative of the other, allowing for quick calculations and simplifications. In the given expression, (7x + 4y)(7x - 4y) can be recognized as a difference of squares.
Recommended video:
06:24Solving Quadratic Equations by Completing the Square
Algebraic Simplification
Algebraic simplification is the process of reducing an expression to its simplest form by combining like terms and applying algebraic identities. This is crucial in making complex expressions easier to work with and understand. After applying the difference of squares to the expression (7x + 4y)(7x - 4y), the result can be simplified to 49x² - 16y², showcasing the importance of this concept.
Recommended video:
Guided course
05:09Introduction to Algebraic Expressions
Related Videos
Related Practice