Squaring Products and Factors
1 When we square a product, we square each factor in the product. For example (4b)2= 16b2. Explain why we cannot square a sum by simply squaring each term of the sum. For example, (a + b)2 is not equal to a2 + b2. Provide appropriate examples.
2 Take a number. Add 1. Square the result. Then subtract from that result the product of the original number times two more than the original number. What did you get? I claim you will always get 1. Can you explain?
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Solution Preview
1.)Because,
(a+b)^2 = (a+b)*(a+b)
Now, by distribution law,
=> (a+b)^2 = a*(a+b) + b*(a+b) = a*a + a*b + b*a + b*b
=> (a+b)^2 = a^2 + ...
Solution Summary
There are two problems here regarding squaring numbers.
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