Question

Error Analysis: Determine which step the first mistake was made in.
Simplify:
y
2
−
2
y
y
2
−
4
⋅
y
3
(
y
+
3
)
y
2
Step 1:
y
(
y
−
2
)
(
y
−
2
)
(
y
−
2
)
⋅
y
3
(
y
+
3
)
y
2
Step 2:
y
(
y
−
2
)
(
y
−
2
)
(
y
−
2
)
⋅
y
⋅
y
⋅
y
(
y
+
3
)
y
⋅
y
Step 3 :
y
2
(
y
+
3
)
(
y
−
2
)
(10 points)
Step 1
Step 2
Step 3
No error was made. All work is correct.

Answer 1

Step 1.

Reason: the denominator y^2 − 4 was treated as (y − 2)(y − 2), but y^2 − 4 = (y − 2)(y + 2).

Correct simplification:
(y^2 − 2y)/(y^2 − 4) * (y^3(y+3))/y^2
= [y(y−2)]/[(y−2)(y+2)] * [y^3(y+3)]/y^2
Cancel (y−2) and simplify y^3/y^2:
= y/(y+2) * y(y+3) = y^2(y+3)/(y+2),

with y ≠ −2, 0, 2.