Answer:
1. N
2. N
3. P
4. P
5. P
6. P
7. N
8. N
9. N
10. P
Step-by-step explanation:
To check if the expression is a perfect square trinomial, it follows that
b² = 4ac
1. m²-4m-4
a = 1, b = -4, c= -4
(-4)² = 4(1)(-4)
16 = -16
N - not a perfect square trinomial
2. 4k² - 8k +2
a = 4, b = -8, c = 2
(-8)² = 4(4)(2)
64 = 32
N -not a perfect square trinomial
3. 4m² - 4m + 1
a = 4, b = -4, c = 1
(-4)² = 4(4)(1)
16 = 16
P - perfect square trinomial
4. 9m² - 6m + 1
a = 9, b = -6, c=1
(-6)² = 4(9)(1)
36 = 36
5. 4X² + 4X + 1
a = 4, b=4, c=1
(4)² = 4(4)(1)
6. 9w² - 12w + 4
a = 9, b= -12, c = 4
(-12)² = 4(9)(4)
144 = 144
7. 81z^4 - 18z² - 1
a = 81, b = -18, c = -1
(-18)² = 4(81)(-1)
324 = -324
8. 64q^6 + 8q³k^4 + k^4
Get the square root of the 1st term and the last term
(8q³ + k²)
Expand: 64q^6 + 16q³k² + k^4
9. q^9 - 8q³k² + 4k^4
Get the square root of the 1st and the last terms
(q^9)^(1/2) = q^(9/2)
4k^4 = 2k²
Since the first term's square root can't be extracted, then it's not a perfect square trinomial
10. 16b^6 + 8b³k² + k^4
Get the square root of both the 1st and the last terms
16b^6 = 4b³
k^4 = k²
Get the middle term to check
(4b³ + k²)² = 16b^6 + 8b³k² + k^4
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Answers & Comments
Answer:
1. N
2. N
3. P
4. P
5. P
6. P
7. N
8. N
9. N
10. P
Step-by-step explanation:
To check if the expression is a perfect square trinomial, it follows that
b² = 4ac
1. m²-4m-4
a = 1, b = -4, c= -4
(-4)² = 4(1)(-4)
16 = -16
N - not a perfect square trinomial
2. 4k² - 8k +2
a = 4, b = -8, c = 2
(-8)² = 4(4)(2)
64 = 32
N -not a perfect square trinomial
3. 4m² - 4m + 1
a = 4, b = -4, c = 1
(-4)² = 4(4)(1)
16 = 16
P - perfect square trinomial
4. 9m² - 6m + 1
a = 9, b = -6, c=1
(-6)² = 4(9)(1)
36 = 36
P - perfect square trinomial
5. 4X² + 4X + 1
a = 4, b=4, c=1
(4)² = 4(4)(1)
16 = 16
P - perfect square trinomial
6. 9w² - 12w + 4
a = 9, b= -12, c = 4
(-12)² = 4(9)(4)
144 = 144
P - perfect square trinomial
7. 81z^4 - 18z² - 1
a = 81, b = -18, c = -1
(-18)² = 4(81)(-1)
324 = -324
N - not a perfect square trinomial
8. 64q^6 + 8q³k^4 + k^4
Get the square root of the 1st term and the last term
(8q³ + k²)
Expand: 64q^6 + 16q³k² + k^4
N - not a perfect square trinomial
9. q^9 - 8q³k² + 4k^4
Get the square root of the 1st and the last terms
(q^9)^(1/2) = q^(9/2)
4k^4 = 2k²
Since the first term's square root can't be extracted, then it's not a perfect square trinomial
N - not a perfect square trinomial
10. 16b^6 + 8b³k² + k^4
Get the square root of both the 1st and the last terms
16b^6 = 4b³
k^4 = k²
Get the middle term to check
(4b³ + k²)² = 16b^6 + 8b³k² + k^4
P - perfect square trinomial