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Chapter 0: Problem 100

Explain how to find the product of the sum and difference of two terms. Give an example with your explanation.

Short Answer

Expert verified
The product of the sum (a+b) and the difference (a-b) of two terms (a and b) is equal to the difference of the squares of the two terms, i.e., \(a^2 - b^2\). For example, with a=5 and b=3, both (5+3)(5-3) and \(5^2 - 3^2\) produce 16.

Step by step solution

01

Understand the Formula

First, become familiar with the formula \( (a+b)(a-b) = a^2 - b^2 \). This is also known as the difference of squares formula. The left-hand side of the formula means multiplying the sum 'a + b' and difference 'a - b' of two numbers 'a' and 'b'. The right-hand side of the formula means subtracting the square of second number 'b' from the square of the first number 'a'.
02

Assist the Formula with An Example

To better understand the formula, an example is really effective. Let's consider a' = 5 and b' = 3. Now, putting these numbers into our formula, on the left side we get \( (5+3)(5-3) = 8*2 = 16 \), and on the right side we get \( 5^2 - 3^2 = 25 - 9 = 16 \). Both sides of the formula yielded the same result, 16, demonstrating that the formula is accurate.
03

Conclusion

The product of the sum and the difference of two numbers is the difference of the squares of the two numbers. This algebraic formula is applicable for any real numbers.

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Most popular questions from this chapter

Find the intersection of the sets. $$\\{1,3,7\\} \cap(2,3,8)$$

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a. A mathematics professor recently purchased a birthday cake for her son with the inscription $$\text { Happy }\left(2^{\frac{5}{2}} \cdot 2^{\frac{3}{4}} \div 2^{\frac{1}{4}}\right) \text { th Birthday. }$$ How old is the son? b. The birthday boy, excited by the inscription on the cake, tried to wolf down the whole thing. Professor Mom, concerned about the possible metamorphosis of her son into a blimp, exclaimed, "Hold on! It is your birthday, so why not take \(\frac{8^{-\frac{4}{3}}+2^{-2}}{16^{-\frac{3}{4}}+2^{-1}}\) of the cake? I'll eat half of what's left over." How much of the cake did the professor eat?

$$\frac{1}{2}+\frac{2}{3}$$
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