Question

Find the value of 513^3-512^3

Answer 1

Answer:

513*513=263169

512*512=262144

513*513-512*512=1025

Step-by-step explanation:

Answer 2

Answer:

787969

Step-by-step explanation:

In general by putting the values simply, will turn this complex and take a lot of time. So we can use the formula of difference of cubes

${x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} )$

So, as the numbers are 513 and 512 , the resultant expression is

$(513 - 512)( {513}^{2} + 513 \times 512 + {512}^{2} )$

which in turn gives

${513}^{3} - {513}^{3} = {513}^{2} + 512 \times 513 + {512}^{2}$

now we know 512=513-1 so

${513}^{2} + 513 \times 512 + {(513 - 1)}^{2} \\ = {513}^{2} + 513 \times 512 + {513}^{2} - 2 \times 513 + 1$

now we see

$2 \times {513}^{2} + 513 \times 510 + 1$

As you know, everything in maths can't be simplified further. So we have to evaluate this expression to get the result. Upon evaluation, the expression gives us the result 787969

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