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

Jul 10, 2018

${\left(x + 5\right)}^{2}$

Explanation:

Using that

${a}^{2} + 2 a b + {b}^{2} = {\left(a + b\right)}^{2}$
we get

${x}^{2} + 10 x + 25 = {\left(x + 5\right)}^{2}$

Jul 21, 2018

See below:

Explanation:

Perfect square quadratics are of the form

${a}^{2} + 2 a b + {b}^{2}$

In our case, $a = x$ and $b = \sqrt{25}$, or $b = 5$

We can plug these values into our expression to get

${x}^{2} + 2 \cdot x \cdot 5 + {5}^{2}$

This simplifies to

${x}^{2} + 10 x + 25$

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

${\left(x + 5\right)}^{2}$

Hope this helps!

Compare given polynomial with the perfect square:${a}^{2} + 2 a b + {b}^{2} = {\left(a + b\right)}^{2}$

Explanation:

Given that

${x}^{2} + 10 x + 25$

$= {x}^{2} + 2 \left(5\right) x + {\left(5\right)}^{2}$

Above expression is in form of ${a}^{2} + 2 a b + {b}^{2}$ which is a perfect square ${\left(a + b\right)}^{2}$ hence the given expression or polynomial is a perfect square given as

${\left(x + 5\right)}^{2}$