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    Squaring Products and Factors

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    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

    (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.