Question

How do you simplify $5xy\left( {{x}^{2}}+2xy+{{y}^{2}} \right)$?

Answer 1

Hint: To solve this question first we will solve the equation inside the bracket. We will use the algebraic formula ${{\left( a+b \right)}^{2}}={{a}^{2}}+2ab+{{b}^{2}}$ to solve the given equation. Then by simplifying the obtained equation we get the desired answer.

Complete step by step solution:
We have been given an equation $5xy\left( {{x}^{2}}+2xy+{{y}^{2}} \right)$.
We have to simplify the given equation.
To solve the given equation first we will solve the brackets.
Now, we know that ${{\left( a+b \right)}^{2}}={{a}^{2}}+2ab+{{b}^{2}}$
Now, comparing the terms inside the bracket we will get
$a=x$ and $y=b$
Now, applying the formula to the given equation we will get
$\Rightarrow 5xy{{\left( x+y \right)}^{2}}$
Now, simplifying the above obtained equation we will get
$\Rightarrow 5xy\left( x+y \right)\left( x+y \right)$
Hence above is the required simplified form of the given equation.

Note: When more than one mathematical operator is given in the equation we have to follow the BODMAS rule to solve the equation. The BODMAS rule tells us about the sequence of mathematical operators the equation has. We have to simplify the bracket first, then power or order, then division, then multiplication, then addition or subtraction. Alternatively students may simplify the given equation as:
$\Rightarrow 5xy\left( {{x}^{2}}+2xy+{{y}^{2}} \right)$
Multiplying the terms inside the bracket by $5xy$ we will get
$\Rightarrow 5{{x}^{3}}y+10{{x}^{2}}{{y}^{2}}+5x{{y}^{3}}$
But it becomes too lengthy to again simplify the obtained equation. So try to follow the method explained in the solution.