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1 answer:
Factor the following:
4 p (4 p - 1) - 3 (4 p - 1)^2
Factor 4 p - 1 from 4 p (4 p - 1) - 3 (4 p - 1)^2:
(4 p - 1) (4 p - 3 (4 p - 1))
-3 (4 p - 1) = 3 - 12 p:
(4 p - 1) (4 p + 3 - 12 p)
Grouping like terms, 4 p - 12 p + 3 = 3 + (4 p - 12 p):
(4 p - 1) (3 + (4 p - 12 p))
4 p - 12 p = -8 p:
Answer: (4 p - 1) (-8 p + 3)
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Factor the following:
m (m + n) - 3 m (m + n)^2
Factor m + n out of m (m + n) - 3 m (m + n)^2, resulting in (m + n) (m - 3 m (m + n)^(2 - 1)):
(m + n) (m - 3 m (m + n)^(2 - 1))
2 - 1 = 1:
(m + n) (m - 3 m (m + n))
Factor m out of m - 3 m (m + n), resulting in m (1 - 3 (m + n)):
m (1 - 3 (m + n)) (m + n)
-3 (m + n) = -3 m - 3 n:
Answer: m (m + n) (-3 m - 3 n + 1)
___________________________________________________________Answer : -(-6 + p^2) (-1 - 6 q + p^2 q)
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Factor the following:
6 u^2 (2 u - 5)^2 - 12 u^2 (2 u - 5) (u + 5)
Factor u^2 out of 6 u^2 (2 u - 5)^2 - 12 u^2 (2 u - 5) (u + 5), resulting in u^2 (6 (2 u - 5)^2 - 12 (2 u - 5) (u + 5)):
u^2 (6 (2 u - 5)^2 - 12 (2 u - 5) (u + 5))
(2 u - 5) (2 u - 5) = (2 u) (2 u) + (2 u) (-5) + (-5) (2 u) + (-5) (-5) = 4 u^2 - 10 u - 10 u + 25 = 4 u^2 - 20 u + 25:
u^2 (6 4 u^2 - 20 u + 25 - 12 (2 u - 5) (u + 5))
6 (4 u^2 - 20 u + 25) = 24 u^2 - 120 u + 150:
u^2 (24 u^2 - 120 u + 150 - 12 (2 u - 5) (u + 5))
(u + 5) (2 u - 5) = (u) (2 u) + (u) (-5) + (5) (2 u) + (5) (-5) = 2 u^2 - 5 u + 10 u - 25 = 2 u^2 + 5 u - 25:u^2 (150 - 120 u + 24 u^2 - 122 u^2 + 5 u - 25)
-12 (2 u^2 + 5 u - 25) = -24 u^2 - 60 u + 300:
u^2 (-24 u^2 - 60 u + 300 + 24 u^2 - 120 u + 150)
Grouping like terms, 24 u^2 - 24 u^2 - 60 u - 120 u + 150 + 300 = (-120 u - 60 u) + (24 u^2 - 24 u^2) + (150 + 300):
u^2 ((-120 u - 60 u) + (24 u^2 - 24 u^2) + (150 + 300))
-120 u - 60 u = -180 u:
u^2 (-180 u + (24 u^2 - 24 u^2) + (150 + 300))
150 + 300 = 450:
u^2 (-180 u + (24 u^2 - 24 u^2) + 450)
24 u^2 - 24 u^2 = 0:
u^2 (450 - 180 u)
Factor 90 out of 450 - 180 u:
Answer: u^2×90 (5 - 2 u)
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4 p (4 p - 1) - 3 (4 p - 1)^2
Factor 4 p - 1 from 4 p (4 p - 1) - 3 (4 p - 1)^2:
(4 p - 1) (4 p - 3 (4 p - 1))
-3 (4 p - 1) = 3 - 12 p:
(4 p - 1) (4 p + 3 - 12 p)
Grouping like terms, 4 p - 12 p + 3 = 3 + (4 p - 12 p):
(4 p - 1) (3 + (4 p - 12 p))
4 p - 12 p = -8 p:
Answer: (4 p - 1) (-8 p + 3)
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Factor the following:
m (m + n) - 3 m (m + n)^2
Factor m + n out of m (m + n) - 3 m (m + n)^2, resulting in (m + n) (m - 3 m (m + n)^(2 - 1)):
(m + n) (m - 3 m (m + n)^(2 - 1))
2 - 1 = 1:
(m + n) (m - 3 m (m + n))
Factor m out of m - 3 m (m + n), resulting in m (1 - 3 (m + n)):
m (1 - 3 (m + n)) (m + n)
-3 (m + n) = -3 m - 3 n:
Answer: m (m + n) (-3 m - 3 n + 1)
___________________________________________________________Answer : -(-6 + p^2) (-1 - 6 q + p^2 q)
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Factor the following:
6 u^2 (2 u - 5)^2 - 12 u^2 (2 u - 5) (u + 5)
Factor u^2 out of 6 u^2 (2 u - 5)^2 - 12 u^2 (2 u - 5) (u + 5), resulting in u^2 (6 (2 u - 5)^2 - 12 (2 u - 5) (u + 5)):
u^2 (6 (2 u - 5)^2 - 12 (2 u - 5) (u + 5))
(2 u - 5) (2 u - 5) = (2 u) (2 u) + (2 u) (-5) + (-5) (2 u) + (-5) (-5) = 4 u^2 - 10 u - 10 u + 25 = 4 u^2 - 20 u + 25:
u^2 (6 4 u^2 - 20 u + 25 - 12 (2 u - 5) (u + 5))
6 (4 u^2 - 20 u + 25) = 24 u^2 - 120 u + 150:
u^2 (24 u^2 - 120 u + 150 - 12 (2 u - 5) (u + 5))
(u + 5) (2 u - 5) = (u) (2 u) + (u) (-5) + (5) (2 u) + (5) (-5) = 2 u^2 - 5 u + 10 u - 25 = 2 u^2 + 5 u - 25:u^2 (150 - 120 u + 24 u^2 - 122 u^2 + 5 u - 25)
-12 (2 u^2 + 5 u - 25) = -24 u^2 - 60 u + 300:
u^2 (-24 u^2 - 60 u + 300 + 24 u^2 - 120 u + 150)
Grouping like terms, 24 u^2 - 24 u^2 - 60 u - 120 u + 150 + 300 = (-120 u - 60 u) + (24 u^2 - 24 u^2) + (150 + 300):
u^2 ((-120 u - 60 u) + (24 u^2 - 24 u^2) + (150 + 300))
-120 u - 60 u = -180 u:
u^2 (-180 u + (24 u^2 - 24 u^2) + (150 + 300))
150 + 300 = 450:
u^2 (-180 u + (24 u^2 - 24 u^2) + 450)
24 u^2 - 24 u^2 = 0:
u^2 (450 - 180 u)
Factor 90 out of 450 - 180 u:
Answer: u^2×90 (5 - 2 u)
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The answer is below
Step-by-step explanation:
Two triangles are said to be congruent if for the two triangles all the three sides are equal and all the three angles are equal to each other.
Given that ΔPQR is congruent to ΔSTU, hence all corresponding sides and corresponding angles are equal to each other.
∠P = ∠S = 59°
∠S + ∠T + ∠U = 180° (sum of angles in a triangle)
59 + 75 + ∠U = 180°
134 + ∠U = 180°
∠U = 46°
∠U = ∠R = 46°
∠Q = ∠T = 75°
Also, for the sides:
ST = PQ = 7 m
SU = PR = 8 m
Answer:
4
Explanation:
I’ve attached my work
Hope it helps, Let me know if you have anymore questions/concerns !
Have a nice rest of your day :)
4
Explanation:
I’ve attached my work
Hope it helps, Let me know if you have anymore questions/concerns !
Have a nice rest of your day :)