Question

How do you translate to an algebraic expression: twice the sum of x and y?

Answer 1

Hint: We first try to make the given written statement in its mathematical form. We have two variables $x$ and $y$ for the addition. Then we add those terms. We follow the multiplication process for signs and find the right sign for the multiplication. Then we need to multiply 2 to the additional value. We get the mathematical statement as the solution.

Complete step-by-step solution:
The given statement is that we need to find the mathematical form of the expression twice the sum of x and y.
We first take addition of those two numbers as variables. Those numbers are $x$ and $y$.
We need to find the added value of those numbers which is $x+y$.
We follow the multiplication process for signs and find the right sign for the multiplication.
Now we need to multiply the addition value with 2.
That’s why we multiply 2 with $x+y$.
The final solution is $$2\times (x+y)=2(x+y)$$.
Therefore, the final algebraic expression of twice the sum of x and y is $$2(x+y)$$.
We can also find the simplified form using a distributive theorem.
The theorem gives that $$2(x+y)=2x+2y$$.

Note: We can verify the result by taking two values for $x$ and $y$ for the expression. We take $x=2$ and $y=1$.
We have to find the multiplied form of $$2(x+y)$$.
This gives $$2(x+y)=2(2+1)=2\times 3=6$$.