Ch. P - Fundamental Concepts of Algebra

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

Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

Problem 83

Chapter 1, Problem 83

In Exercises 83–90, perform the indicated operation or operations. (3x+4y)²−(3x−4y)²

Verified step by step guidance

Recognize that the given expression involves the difference of two squares: $(3x + 4y)^2 - (3x - 4y)^2$. The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$.

Identify $a = (3x + 4y)$ and $b = (3x - 4y)$ in the expression. Substitute these into the difference of squares formula.

Apply the formula: $(3x + 4y) - (3x - 4y)$ and $(3x + 4y) + (3x - 4y)$. Simplify each term inside the parentheses.

Simplify $(3x + 4y) - (3x - 4y)$ to $8y$ and $(3x + 4y) + (3x - 4y)$ to $6x$.

Multiply the simplified terms: $8y \cdot 6x$. This gives the final simplified expression, which you can calculate if needed.

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.

Binomial Expansion

Binomial expansion refers to the process of expanding expressions that are raised to a power, particularly those in the form (a + b)^n. The expansion can be achieved using the Binomial Theorem, which states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where k ranges from 0 to n. This concept is essential for simplifying expressions like (3x + 4y)^2.

Difference of Squares

The difference of squares is a specific algebraic identity that states a^2 - b^2 = (a - b)(a + b). This identity is useful for factoring expressions where two squared terms are subtracted. In the given problem, recognizing that the expression can be treated as a difference of squares will simplify the calculation significantly.

Factoring

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. This technique is crucial in algebra for simplifying expressions and solving equations. In this case, after applying the difference of squares, factoring will help in obtaining the final simplified form of the expression.

Recommended video:

Guided course

04:36

Factor by Grouping

Related Practice

Textbook Question

Write each number in scientific notation. −3829

Textbook Question

Add or subtract terms whenever possible. √3+³√15

Textbook Question

State the name of the property illustrated. 1/(x+3) (x+3)=1, x≠−3

Textbook Question

Perform the indicated operations. Indicate the degree of the resulting polynomial. $(13 x^{3} y^{2} - 5 x^{2} y - 9 x^{2}) - (- 11 x^{3} y^{2} - 6 x^{2} y + 3 x^{2} - 4)$

Textbook Question

Perform the indicated operations. Indicate the degree of the resulting polynomial. $(7 x^{2} - 8 x y + y^{2}) + (- 8 x^{2} - 9 x y - 4 y^{2})$

Textbook Question

Evaluate each expression without using a calculator. 36^1/2

views

In Exercises 83–90, perform the indicated operation or operations. (3x+4y)2−(3x−4y)2

Verified video answer for a similar problem:

Key Concepts

Binomial Expansion

Difference of Squares

Factoring

In Exercises 83–90, perform the indicated operation or operations. (3x+4y)²−(3x−4y)²