Question 20

If $$A = 125$$ and $$B = 8$$, then what is the value of

$$(A + B)^3 - (A - B)^3 - 6B(A^2 - B^2)$$?

Solution

$$(A+B)^3-(A-B)^3-6B(A^2-B^2)$$

$$=\left(A+B-A+B\right)^3+3\left(A+B\right)\left(A-B\right)\left(A+B-A+B\right)-6B\left(A^2-B^2\right).$$

$$=\left(2B\right)^3+6\left(A^2-B^2\right)B-6B\left(A^2-B^2\right).$$

$$=\left(2\times8\right)^3=4096.$$

A is correct choice.

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