Question

Perform the operations and simplify. $$(3 m+4 n)(3 m-4 n)$$

   Perform the operations and simplify. $$(3 m+4 n)(3 m-4 n)$$

College Algebra

College Algebra

R. David Gustafson,… 11th Edition

Chapter 0, Problem 55

Instant Answer

Solved by Expert Matt Gibson

07/15/2020

Step 1

This is a difference of squares pattern, which can be simplified as $(a+b)(a-b) = a^2 - b^2$. Show more…

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Perform the operations and simplify. $$(3 m+4 n)(3 m-4 n)$$

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Key Concepts

Difference of Squares

This is an algebraic identity which states that the product of the sum and difference of the same two terms (a + b)(a - b) will always equal the difference of their squares, a² - b². Recognizing this pattern simplifies multiplication and factoring in algebra.

Algebraic Identities

These are established formulas that provide shortcuts for simplifying algebraic expressions. The difference of squares is one such identity, and it is integral for quickly reducing expressions that fit its pattern.

Polynomial Multiplication

This concept involves multiplying terms in two or more polynomials, where the distributive property is applied to ensure that every term in the first expression is multiplied by every term in the second. It underpins the process of expanding and simplifying expressions like the product of binomials.

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