Question

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Explain, in complete sentences, the effect of the difference of squares pattern on the multiplication of radicals. Give an example.

Answer 1

The product of a sum and a difference of two values is equal to the difference of their squares.
If both of those quantities are square roots of integers, for example p and q
such that a = √p and b = √q
then performing the expansion squares the radicals leaving only integers.
(√p + √q)(√p - √q) = (a + b)(a - b) = a^2 - b^2 = p - q

If only one of the quantities is a square root of an integer we get
(p + √q)(p - √q) = (a^2 + b)(a^2 - b) = a^4 - b^2 = p^2 - q

Answer 2

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