Question

If m/n = 5, then what is the value of m^2 - 25n^2?

Answer 1

Answer: 0

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Work Shown:

m/n = 5

m = 5n

m^2 - 25n^2 = (m)^2 - (5n)^2

m^2 - 25n^2 = (m-5n)(m+5n)

m^2 - 25n^2 = (5n-5n)(5n+5n)

m^2 - 25n^2 = (0n)(10n)

m^2 - 25n^2 = (0)(10n)

m^2 - 25n^2 = 0

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Another approach:

m/n = 5

m = 5n

m^2 = (5n)^2

m^2 = 25n^2

m^2 - 25n^2 = 0

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Consider the example that m = 10 and n = 2.

We can see that m/n = 10/2 = 5

Furthermore,

m^2 - 25n^2 = 10^2 - 25*2^2 = 100 - 100 = 0

I'll let you try out other examples.