Question

What is a simplified eCarlotta thinks that 3y + 5y3 is the same as 8y4. Which statement shows that it is NOT the same?Xpression for (x + y) – (x – y)?

Answer 1

Questions:

(a) What is a simplified expression for (x + y) – (x – y)?

(b) Carlotta thinks that
`3y + 5y^3` is the same as
`8y^4`. Which statement shows that it is NOT the same?

Answer:

`(x + y) - (x - y) =2y`

`3y + 5y^3 \\e 8y^4`

Explanation:

Solving (a):

Given

`(x + y) - (x - y)`

Required

Simplify

`(x + y) - (x - y)`

Open brackets

`(x + y) - (x - y) = x + y - x + y`

Collect Like Terms

`(x + y) - (x - y) = x - x+ y + y`

`(x + y) - (x - y) = y + y`

`(x + y) - (x - y) =2y`

Solving (b):

Given

`3y + 5y^3` and
`8y^4`

Required

Which expression shows they are not the same

The expression that shows this is:

`3y + 5y^3 \\e 8y^4`

Take for instance; y=2

Substitute 2 for y in
`3y + 5y^3 \\e 8y^4`

`3*2 + 5*2^3 \\e 8*2^4`

Evaluate all exponents

`9 + 5*8 \\e 8*16`

`9 + 40 \\e 128`

`49 \\e 128`

The above expression supports
`3y + 5y^3 \\e 8y^4`