You should know that:
(a+b)(a+b)(a+b)
=a(a+b)(a+b)+b(a+b)(a+b)
=a(a²+2ab+b²)+b(a²+2ab+b²)
=a³+2a²b+ab²+a²b+2ab²+b³
=a³+3a²b+3ab²+b³
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If a=5x and b=-4y
(5x+(-4y))³
=(5x-4y)³
=(5x)³+3(5x)²(-4y)+3(5x)(-4y)²+(-4y)³
=125x³+3(25x²)(-4y)+15x(16y²)-64y³
=125x³+75x²(-4y)+240xy²-64y³
=125x³-300x²y+240xy²-64y³
To get the *percent increase* from week 1 to week 2, we calculate the change in distance from week 1 to week 2 (13.5 - 12.5 = 1 mile) over the week 1 distance (12.5 miles). Doing that, we find that Matthew increased his distance by
1/12.5 = 0.08, or 8%
We’re given that he’ll increase his distance by the same percentage from week 2 to 3, so to find his week 3 distance, we can find 8% of the week 2 distance and add that on. 8% of 13.5 miles is 0.08 x 13.5 = 1.08 miles, so by week 3, he’ll be running 13.5 + 1.08 = 14.58 miles.