How do you simplify (2y + 5x)^2?

Jan 21, 2017

You can Distribute by rewriting:$\left(2 y + 5 x\right) \left(2 y + 5 x\right)$
which produces: $4 {y}^{2} + 10 x y + 10 x y + 25 {x}^{2}$.

Explanation:

Combine the like terms in the "middle" :
$4 {y}^{2} + 20 x y + 25 {x}^{2}$

If you want a challenge, you can do this in your head:
1) Square the first term 2y: ${2}^{2} {y}^{2}$= $4 {y}^{2}$

2) Take the product of the terms: $2 y \cdot 5 x$ = $10 x y$ and double it!
$2 \cdot 10 x y = 20 x y$

3) Square the second term: ${5}^{2} {x}^{2} = 25 {x}^{2}$

4) and combine! $4 {y}^{2} + 20 x y + 25 {x}^{2}$

Jan 21, 2017

See the entire simplification process below:

Explanation:

First, rewrite this expression as:

$\left(2 y + 5 x\right) \left(2 y + 5 x\right)$

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{2 y} + \textcolor{red}{5 x}\right) \left(\textcolor{b l u e}{2 y} + \textcolor{b l u e}{5 x}\right)$ becomes:

$\left(\textcolor{red}{2 y} \times \textcolor{b l u e}{2 y}\right) + \left(\textcolor{red}{2 y} \times \textcolor{b l u e}{5 x}\right) + \left(\textcolor{red}{5 x} \times \textcolor{b l u e}{2 y}\right) + \left(\textcolor{red}{5 x} \times \textcolor{b l u e}{5 x}\right)$

$4 {y}^{2} + 10 x y + 10 x y + 25 {x}^{2}$

We can now combine like terms:

$4 {y}^{2} + \left(10 + 10\right) x y + 25 {x}^{2}$

$4 {y}^{2} + 20 x y + 25 {x}^{2}$