Textbook Question
In Exercises 39–48, factor the difference of two squares. x^2−144
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0. Review of Algebra
Factoring Polynomials
1:49 minutesProblem 42
Textbook Question
Factor the difference of two squares.
Verified step by step guidance1
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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1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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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.
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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.
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