Question 126345
The given expression falls under the following factoring rule:
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{{{X^2 - Y^2 = (X - Y)*(X + Y)}}}
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In the given expression note that X = 2a because when you square both sides you get {{{X^2 = 4a^2}}}
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Also note that Y = 6b because when you square both sides you get {{{Y^2 = 36b^2}}}
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Substituting 2a for X and 6b for Y in the factoring rule leads to:
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{{{(2a)^2 - (6b)^2 = (2a - 6b)*(2a + 6b)}}}
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Then notice on the right side that each of the two factors has 2 as a common factor of the
two terms in parentheses. This means that each factor on the right side can have a 2 factored
from it, and this leads to:
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{{{(2a)^2 - (6b)^2 = 2*(a - 3b)*2*(a + 3b)}}}
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Multiply the two factors of 2 to get 4 and you have the final answer of:
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{{{(2a)^2 - (6b)^2 = 4*(a - 3b)*(a + 3b)}}}
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If you like, you can then square out the two terms on the left side and you have:
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{{{4a^2 - 36b^2 = 4*(a - 3b)*(a + 3b)}}}
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Hope this helps you understand how to do the problem, and how to use the rule that applies.
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