Fill up the gap #49x^2-square+25# to make it a perfect square?

1 Answer
Jan 26, 2017

Answer is #70x#, which makes #49x^2-70x+25=(7x-5)^2#

Explanation:

Let us recall the formula #a^2-2ab+b^2=(a-b)^2#.

Here, we have first term as square of #a#, third term is also square of another term #b#,

and middle term is #2ab#, which is product of the terms #a# and #b# and ten multiplied by #2# #-># and then result is square of first term minus second term.

In #49x^2-?+25#, what we have as first term is #49x^2#, which is square of #7x#,

we also have third term as #25#, which is square of #5#.

Hence, middle term ought to be #7x xx 5 xx2=70x# and hence we should replace ? by #70x# to make it square

i.e. #49x^2-70x+25# and then it becomes #(7x-5)^2#