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Chapter 5: Problem 7

Factorise \(\alpha^{2}-\beta^{2}\)

Short Answer

Expert verified
Answer: \((\alpha+\beta)(\alpha-\beta)\)

Step by step solution

01

Identify the base terms in the difference of squares

Identify the base terms in the expression, which are \(\alpha\) and \(\beta\). These will be used as the variables in the \((a+b)(a-b)\) formula.
02

Apply the difference of squares formula

Using the difference of squares formula, apply it with \(\alpha\) and \(\beta\) as our variables. The formula is \((a+b)(a-b)\), so we will substitute \(\alpha\) for \(a\) and \(\beta\) for \(b\) to get \((\alpha+\beta)(\alpha-\beta)\).
03

Present the factorised expression

Now that we have substituted and used the difference of squares formula, the factorised expression should resemble the following: $$ \alpha^{2}-\beta^{2} = (\alpha+\beta)(\alpha-\beta) $$

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