Factor the difference of two squares. 64x2−$$8164x^2$$−81

Ch. P - Fundamental Concepts of Algebra

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Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

문제 42

1장, 문제 42

Factor the difference of two squares. $64 x squared minus 81$

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Recognize that the expression $64x^2 - 81$ is a difference of two squares because it can be written as $(8x)^2 - 9^2$.

Recall the difference of squares formula: $a^2 - b^2 = (a - b)(a + b)$.

Identify $a = 8x$ and $b = 9$ from the expression.

Apply the formula by substituting $a$ and $b$: $(8x - 9)(8x + 9)$.

Write the factored form of the expression as $(8x - 9)(8x + 9)$.

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주요 개념

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Difference of Squares

The difference of squares is a specific algebraic expression of the form a² - b², which can be factored into (a - b)(a + b). Recognizing this pattern allows for straightforward factoring of expressions where two perfect squares are subtracted.

Identifying Perfect Squares

To factor using the difference of squares, each term must be a perfect square. This means the terms can be expressed as the square of a number or variable, such as 64x² = (8x)² and 81 = 9², enabling the use of the difference of squares formula.

Factoring Polynomials

Factoring polynomials involves rewriting an expression as a product of simpler expressions. Understanding how to factor special forms like the difference of squares is essential for simplifying expressions and solving equations in algebra.

Factor the difference of two squares. 64x2−8164x^2−81