?You can use the product of conjugates pattern to multiply numbers without a calculator

Chapter 6, Problem 350

(choose chapter or problem)

You can use the product of conjugates pattern to multiply numbers without a calculator. Say you need to multiply 47 times 53. Think of 47 as 50 − 3 and 53 as 50 + 3 .

ⓐ Multiply (50 − 3)(50 + 3) by using the product of conjugates pattern, \((a-b)(a+b)=a^{2}-b^{2}\).

ⓑ Multiply \(47 \cdot 53\) without using a calculator.

ⓒ Which way is easier for you? Why?

Text Transcription:

(a-b)(a+b)=a^2-b^2

47 dot 53

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