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:

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

$3y + 5y^3 \ne 8y^4$

Step-by-step 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:

$3y + 5y^3 \ne 8y^4$

Take for instance; y=2

Substitute 2 for y in $3y + 5y^3 \ne 8y^4$

$3*2 + 5*2^3 \ne 8*2^4$

Evaluate all exponents

$9 + 5*8 \ne 8*16$

$9 + 40 \ne 128$

$49 \ne 128$

The above expression supports $3y + 5y^3 \ne 8y^4$