Question

How do you find the product \[{{\left( 8h-4n \right)}^{2}}\] ?

Answer 1

Hint: For such problems we need to have a general basic as well as to some extent a bit of advanced knowledge of factorisation, factor theorem, algebraic multiplication and expansion of series. We must also know that whenever we are given something to the power of some number that is equivalent to the index multiplied by itself a number of times which is equal to the power. We must perform simple algebraic multiplication while solving this particular problem. Here there are two unknown parameters given, whose value cannot be determined because we do not have any equation which equates to a value.

Complete step by step answer:
Now we start off with the solution to the given problem by writing that,
We can rearrange the given problem as,
\[\Rightarrow {{\left( 8h-4n \right)}^{2}}=\left( 8h-4n \right)\times \left( 8h-4n \right)\]
Now from this above step we perform simple algebraic multiplication and write it as,
\[\Rightarrow {{\left( 8h-4n \right)}^{2}}=64{{h}^{2}}-32hn-32hn+16{{n}^{2}}\]
Now we add all the like terms from the above step to get,
\[\Rightarrow {{\left( 8h-4n \right)}^{2}}=64{{h}^{2}}-64hn+16{{n}^{2}}\]

Thus, from the above we can clearly say that the expansion of the given problem is \[64{{h}^{2}}-64hn+16{{n}^{2}}\]

Note: For such problems we need to be through about the concepts of algebra which includes factorisation and expansions. We apply the general formulae of square or cube of two numbers which we have studied in our elementary level. However this particular problem can also be solved using the normal method for binomial expansion or if we want a cleaner application, we can use the Pascal’s Triangle method to solve it more quickly.