Question

How do you know if `x^2 + 10x + 25` is a perfect square?

Answer 1

`(x+5)^2`

Explanation:

Using that

`a^2+2ab+b^2=(a+b)^2`
we get

`x^2+10x+25=(x+5)^2`

Answer 2

See below:

Explanation:

Perfect square quadratics are of the form

`a^2+2ab+b^2`

In our case, `a=x` and `b=sqrt25`, or `b=5`

We can plug these values into our expression to get

`x^2+2*x*5+5^2`

This simplifies to

`x^2+10x+25`

Solidifying the fact that this is a perfect square, since `5` and `5` sum up to `10` and have a product of `25`, we can factor this as

`(x+5)^2`

Hope this helps!

Answer 3

Compare given polynomial with the perfect square:`a^2+2ab+b^2=(a+b)^2`

Explanation:

Given that

`x^2+10x+25`

`=x^2+2(5)x+(5)^2`

Above expression is in form of `a^2+2ab+b^2` which is a perfect square `(a+b)^2` hence the given expression or polynomial is a perfect square given as

`(x+5)^2`