Question

Translate the following phrases into algebraic expressions. Explain, in complete sentences, the difference between the two.
• twice the sum of x and y
• the sum of twice x and y

Answer 1

1.. x plus (add) y squared (multiply by itself)
x + y*y
= x + y^2

2. 8 times(multiply) a number, x, decreased (subtract) by y
8x - y
3. the sum (add) of x and y, squared
x + y*y
=x + y^2
4. 3 times(multiply) the difference (subtract) of x and y
=3( x + y)
5. 6 less than (subtract) x cubed
6 - x*x*x
=6 - x^3

* twice the sum(addition) of x and y
=2(x + y)
* the sum(addition) of twice x and y
=2x + y
First means two times x added to 2 times y
Second means two times x added to y only.
There is a difference of a y between them.