Question

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

Answer 1

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`