# How do you multiply (4x + 5)^2?

Nov 27, 2017

$16 {x}^{2} + 40 x + 25$

#### Explanation:

${\left(4 x + 5\right)}^{2} = \left(4 x + 5\right) \left(4 x + 5\right)$

$\text{each term in the second factor is multiplied by }$
$\text{each term in the first factor}$

$\Rightarrow \left(\textcolor{red}{4 x + 5}\right) \left(4 x + 5\right)$

$= \textcolor{red}{4 x} \left(4 x + 5\right) \textcolor{red}{+ 5} \left(4 x + 5\right)$

$\text{distribute each product}$

$= 16 {x}^{2} + 20 x + 20 x + 25$

$= 16 {x}^{2} + 40 x + 25 \leftarrow \textcolor{b l u e}{\text{collect like terms}}$

Nov 27, 2017

$16 {x}^{2} + 40 x + 25$

#### Explanation:

Use the FOIL method, or the shortcut for squaring binomials.

For any $x$ and $y$, ${\left(x + y\right)}^{2} = {x}^{2} + 2 x y + {y}^{2}$

Our $x$ is $4 x$ and our $y$ is $5$.

Therefore:

${\left(4 x + 5\right)}^{2} = {\left(4 x\right)}^{2} + 2 \left(4 x \cdot 5\right) + {\left(5\right)}^{2}$

${\left(4 x + 5\right)}^{2} = 16 {x}^{2} + 40 x + 25$

Alternatively, you could multiply 'each by each,' using the FOIL method.

Nov 27, 2017

See a solution process below:

#### Explanation:

We can use this rule for quadratics:

${\left(\textcolor{red}{x} + \textcolor{b l u e}{y}\right)}^{2} = \left(\textcolor{red}{x} + \textcolor{b l u e}{y}\right) \left(\textcolor{red}{x} + \textcolor{b l u e}{y}\right) = {\textcolor{red}{x}}^{2} + 2 \textcolor{red}{x} \textcolor{b l u e}{y} + {\textcolor{b l u e}{y}}^{2}$

Let:

$\textcolor{red}{x} = 4 x$

$\textcolor{b l u e}{y} = 5$

Substituting gives:

${\left(\textcolor{red}{4 x} + \textcolor{b l u e}{5}\right)}^{2} \implies$

$\left(\textcolor{red}{4 x} + \textcolor{b l u e}{5}\right) \left(\textcolor{red}{4 x} + \textcolor{b l u e}{5}\right) \implies$

$16 {x}^{2} + 40 x + 25$

Nov 27, 2017

$= 16 {x}^{2} + 40 x + 25$

#### Explanation:

${\left(4 x + 5\right)}^{2}$

As you can see, each users are solving it differently and this is what makes Math funny and unique. There are different steps, strategies you can use to solve a problem.

Well, I'm gonna use my favorite method which is Distributive

So let's start:

$= \left(4 x\right) \left(4 x\right) + \left(4 x\right) \left(5\right) + \left(5\right) \left(4 x\right) + \left(5\right) \left(5\right)$

$= 16 {x}^{2} + 20 x + 20 x + 25$

$= 16 {x}^{2} + 40 x + 25$