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

1 Answer
Shwetank Mauria
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

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