Questions:
(a) What is a simplified expression for (x + y) – (x – y)?
(b) Carlotta thinks that [tex]3y + 5y^3[/tex] is the same as [tex]8y^4[/tex]. Which statement shows that it is NOT the same?
Answer:
[tex](x + y) - (x - y) =2y[/tex]
[tex]3y + 5y^3 \ne 8y^4[/tex]
Step-by-step explanation:
Solving (a):
Given
[tex](x + y) - (x - y)[/tex]
Required
Simplify
[tex](x + y) - (x - y)[/tex]
Open brackets
[tex](x + y) - (x - y) = x + y - x + y[/tex]
Collect Like Terms
[tex](x + y) - (x - y) = x - x+ y + y[/tex]
[tex](x + y) - (x - y) = y + y[/tex]
[tex](x + y) - (x - y) =2y[/tex]
Solving (b):
Given
[tex]3y + 5y^3[/tex] and [tex]8y^4[/tex]
Required
Which expression shows they are not the same
The expression that shows this is:
[tex]3y + 5y^3 \ne 8y^4[/tex]
Take for instance; y=2
Substitute 2 for y in [tex]3y + 5y^3 \ne 8y^4[/tex]
[tex]3*2 + 5*2^3 \ne 8*2^4[/tex]
Evaluate all exponents
[tex]9 + 5*8 \ne 8*16[/tex]
[tex]9 + 40 \ne 128[/tex]
[tex]49 \ne 128[/tex]
The above expression supports [tex]3y + 5y^3 \ne 8y^4[/tex]
