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Chapter 0: Problem 47

Factor the difference of two squares. $$16 x^{4}-81$$

Short Answer

Expert verified
The factorisation of \(16x^4 - 81\) is \((4x^2 + 9)(2x + 3)(2x - 3)\).

Step by step solution

01

Identify the squares

Rewrite the expression \(16x^4 - 81\) as \((4x^2)^2 - (9)^2 \). Here, \(a =4x^2 \) and \(b = 9\).
02

Apply the Difference of Squares formula

Substitute \(a\) and \(b\) into the formula as \((a+b)(a-b) = (4x^2 + 9) (4x^2 - 9)\).
03

Notice the difference of squares again

Notice that the factor \(4x^2 - 9 = (2x)^2 - (3)^2\), which can be factored further by Difference of Squares formula.
04

Apply the Difference of Squares formula again

Substitute \(a =2x\) and \(b = 3\) into the formula as \((a+b)(a-b) = (2x + 3) (2x - 3)\).
05

Final Answer

Combine the factors from Step 2 and Step 4 to get the final factorisation: \((4x^2 + 9)(2x + 3)(2x - 3)\).

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Most popular questions from this chapter

Describe ways in which solving a linear inequality is different than solving a linear equation.

Will help you prepare for the material covered in the next section. Jane's salary exceeds Jim's by \(\$ 150\) per week. If \(x\) represents Jim's weekly salary, write an algebraic expression that models Jane's weekly salary.

Explain how to add rational expressions having no common factors in their denominators. Use \(\frac{3}{x+5}+\frac{7}{x+2}\) in your explanation.

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. On two examinations, you have grades of 86 and \(88 .\) There is an optional final examination, which counts as one grade. You decide to take the final in order to get a course grade of A, meaning a final average of at least 90 . a. What must you get on the final to earn an A in the course? b. By taking the final, if you do poorly, you might risk the B that you have in the course based on the first two exam grades. If your final average is less than \(80,\) you will lose your \(\mathrm{B}\) in the course. Describe the grades on the final that will cause this to happen.

Describe ways in which solving a linear inequality is similar to solving a linear equation.
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