Explanation

Whenever you see exponents, think common quadratics.

If you factor the 6 out of the numerator in Quantity A, you get \(6(a^2 + 2ab + b^2)\), which includes a common quadratic \((a +b)^2\).

Then you can cancel (a + b) from both the numerator and the denominator; Quantity A is really just 6(a + b). The quantities are equal.
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Given:
QUANTITY A: \(\frac{6a^2+12ab+6b^2}{(a+b)}\)

QUANTITY B: \(6(a+b)\)


First factor out the 6 from numerator in Quantity A to get:
QUANTITY A: \(\frac{6(a^2+2ab+b^2)}{(a+b)}\)

QUANTITY B: \(6(a+b)\)


Now factor quadratic in Quantity A to get:
QUANTITY A: \(\frac{6(a+b)(a+b)}{(a+b)}\)

QUANTITY B: \(6(a+b)\)


The \((a+b)\) terms cancel out in the denominator and numerator in Quantity A to get:
QUANTITY A: \(6(a+b)\)
QUANTITY B: \(6(a+b)\)

Answer: C
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