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

Jan 26, 2017

Answer is $70 x$, which makes $49 {x}^{2} - 70 x + 25 = {\left(7 x - 5\right)}^{2}$

#### Explanation:

Let us recall the formula ${a}^{2} - 2 a b + {b}^{2} = {\left(a - b\right)}^{2}$.

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

and middle term is $2 a b$, which is product of the terms $a$ and $b$ and ten multiplied by $2$ $\to$ and then result is square of first term minus second term.

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

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

Hence, middle term ought to be $7 x \times 5 \times 2 = 70 x$ and hence we should replace ? by $70 x$ to make it square

i.e. $49 {x}^{2} - 70 x + 25$ and then it becomes ${\left(7 x - 5\right)}^{2}$