In Exercises 15–58, find each product. (7x2−2)(3x2−5)

Ch. P - Fundamental Concepts of Algebra

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

All textbooks

Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

Problem 28

Chapter 1, Problem 28

In Exercises 15–58, find each product. (7x²−2)(3x²−5)

Verified step by step guidance

Step 1: Recognize that the problem involves multiplying two binomials, (7x^2 - 2) and (3x^2 - 5). This can be solved using the distributive property, also known as the FOIL method (First, Outer, Inner, Last).

Step 2: Multiply the 'First' terms of each binomial: (7x^2) * (3x^2). This results in 21x^4.

Step 3: Multiply the 'Outer' terms of each binomial: (7x^2) * (-5). This results in -35x^2.

Step 4: Multiply the 'Inner' terms of each binomial: (-2) * (3x^2). This results in -6x^2.

Step 5: Multiply the 'Last' terms of each binomial: (-2) * (-5). This results in +10. Combine all these terms to form the expanded expression: 21x^4 - 35x^2 - 6x^2 + 10. Then simplify by combining like terms.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Polynomial Multiplication

Polynomial multiplication involves distributing each term in the first polynomial to every term in the second polynomial. This process is often referred to as the FOIL method for binomials, but it generalizes to any polynomials. The goal is to combine like terms after distribution to simplify the expression.

Distributive Property

The distributive property states that a(b + c) = ab + ac. This property is fundamental in algebra as it allows for the multiplication of a single term by a sum or difference. In the context of polynomials, it helps in expanding expressions by ensuring that each term is multiplied correctly.

Combining Like Terms

Combining like terms is the process of simplifying an expression by adding or subtracting terms that have the same variable raised to the same power. This step is crucial after multiplying polynomials, as it helps to reduce the expression to its simplest form, making it easier to interpret and work with.

Recommended video:

5:22

Combinations

Related Practice

Textbook Question

Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √48x³/√3x

Textbook Question

Simplify each exponential expression: $(- 5 x^{3} y^{2}) (- 2 x^{- 11} y^{- 2})$

views

Textbook Question

In Exercises 15–32, multiply or divide as indicated. (x²+x)/(x²−4) ÷ (x²−1)/(x²+5x+6)

views

Textbook Question

Simplify each exponential expression in Exercises 23–64. $x^{- 5} \cdot x^{10}$

Textbook Question

Simplify each exponential expression: $(- 2 x^{4} y^{3})^{3}$

views

Textbook Question

Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. $\frac{\sqrt{150 x^{4}}}{\sqrt{3 x}}$

views