Textbook Question
Find each product : (4x+5)(4x-5)
Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 75
Find each product :
Verified step by step guidance1
Identify the two polynomials to be multiplied: \((3x - 2)\) and \((4x^2 + 3x - 5)\).
Apply the distributive property (also known as the FOIL method for binomials) by multiplying each term in the first polynomial by each term in the second polynomial.
Multiply \$3x$ by each term in the second polynomial: \(3x \times 4x^2\), \(3x \times 3x\), and \(3x \times (-5)\).
Multiply \(-2\) by each term in the second polynomial: \(-2 \times 4x^2\), \(-2 \times 3x\), and \(-2 \times (-5)\).
Combine all the products from the previous steps and then simplify by combining like terms to write the final expanded polynomial.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Polynomial Multiplication
Polynomial multiplication involves multiplying each term in one polynomial by every term in the other polynomial. This process requires distributing each term carefully to ensure all products are accounted for, combining like terms afterward to simplify the expression.
Recommended video:
03:42
Finding Zeros & Their Multiplicity
Distributive Property
The distributive property states that a(b + c) = ab + ac. It is essential for multiplying polynomials because it allows you to multiply each term inside the parentheses by the term outside, ensuring all parts of the expression are multiplied correctly.
Recommended video:
Guided course
04:15Multiply Polynomials Using the Distributive Property
Combining Like Terms
After multiplying polynomials, you often get terms with the same variable raised to the same power. Combining like terms means adding or subtracting these terms to simplify the polynomial into its standard form, making it easier to interpret and use.
Recommended video:
5:22Combinations
Related Practice
Textbook Question
In Exercises 67–82, find each product. (9x+7y)2
1
views
Textbook Question
In Exercises 65–92, factor completely, or state that the polynomial is prime. 9x3−9x
1
views
Textbook Question
Add or subtract terms whenever possible.
Textbook Question
Write each number in decimal notation without the use of exponents.
Textbook Question
State the name of the property illustrated. 6+(−4)=(−4)+6
5
views