How do you write x³+8x²+16x in factored form?

Mar 2, 2018

$x \left(x + 4\right) \left(x + 4\right)$

Explanation:

Note that all terms include an instance of $x .$ Thus, we can factor out $x :$

${x}^{3} + 8 {x}^{2} + 16 x = x \left({x}^{2} + 8 x + 16\right)$

We now have a single term and a quadratic equation. Let's factor the quadratic ${x}^{2} + 8 x + 16$.

We must find two numbers, $a$ and $b$, which multiply together to give $16$ and add together to give $8$ to factor our quadratic into the form $\left(x + a\right) \left(x + b\right)$ . Note that $a$ and $b$ can be the same number.

That would be $4 , 4$, as $4 \cdot 4 = 16 , 4 + 4 = 8$

So, the factored form of our quadratic is ${x}^{2} + 8 x + 16 = \left(x + 4\right) \left(x + 4\right)$

$x \left({x}^{2} + 8 x + 16\right) = x \left(x + 4\right) \left(x + 4\right)$