Factor (2a-1/3)^2-(a-5/3)^2

Math
(2a-13)2-(a-53)2
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=2a-13 and b=a-53.
(2a-13+a-53)(2a-13-(a-53))
Simplify.
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Add 2a and a.
(3a-13-53)(2a-13-(a-53))
Combine the numerators over the common denominator.
(3a+-1-53)(2a-13-(a-53))
Subtract 5 from -1.
(3a+-63)(2a-13-(a-53))
Factor 3 out of 3a+-63.
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Factor 3 out of 3a.
(3(a)+-63)(2a-13-(a-53))
Factor 3 out of -63.
(3a+3(-23))(2a-13-(a-53))
Factor 3 out of 3a+3(-23).
3(a+-23)(2a-13-(a-53))
3(a+-23)(2a-13-(a-53))
Apply the distributive property.
3(a+-23)(2a-13-a–53)
Multiply –53.
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Multiply -1 by -1.
3(a+-23)(2a-13-a+1(53))
Multiply 53 by 1.
3(a+-23)(2a-13-a+53)
3(a+-23)(2a-13-a+53)
Subtract a from 2a.
3(a+-23)(a-13+53)
Combine the numerators over the common denominator.
3(a+-23)(a+-1+53)
Add -1 and 5.
3(a+-23)(a+43)
3(a+-23)(a+43)
Factor (2a-1/3)^2-(a-5/3)^2

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