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Chapter 5: Problem 106

Explain how to square a binomial difference. Give an example with your explanation.

Short Answer

Expert verified
To square a binomial difference, apply the Binomial Square rule \((a - b)^2 = a^2 - 2ab + b^2\). For the binomial difference \(4 - 3\), the result when squared is 1.

Step by step solution

01

Understand the Binomial Square Rule

Firstly, you should know that the rule to square a binomial difference is \((a - b)^2 = a^2 - 2ab + b^2\). This rule is derived from the formula \((a - b)(a - b)\), where 'a' and 'b' are any numbers. When squaring a binomial difference, each term is squared and added with a two-time product of the multiplication of both terms.
02

Apply the Rule

Choose a binomial difference to square. For instance, consider the binomial difference \((4 - 3)\). Using the Binomial Square rule, the calculation is done in this way: \((4 - 3)^2 = 4^2 - 2*4*3 + 3^2\).
03

Perform the calculation

Perform each calculation individually. For example \(4^2\) is 16, while the product of \(2*4*3\) is 24, and \(3^2\) is 9. Then find the total by adding and subtracting as appropriate: \(16 - 24 + 9 = 1\). Hence, the square of the binomial difference \((4 - 3)^2\) equals 1.

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Most popular questions from this chapter

Will help you prepare for the material covered in the next section. $$\text { Simplify: } \frac{\left(x^{2}\right)^{3}}{5^{3}}$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Because division by 0 is undefined, numbers to 0 powers should not be written in denominators.

Use the order of operations to evaluate $$x^{3} y+2 x y^{2}+5 x-2$$ for \(x=-2\) and \(y=3\).

Solve for \(W: \quad R=\frac{L+3 W}{2}\). (Section 2.4, Example 4)

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