(p+q)²(b-c) + (p+q)(b-c)² factorise it ........ its urjent
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Answer:
Step-by-step explanation:
Input:
(p + q)^2 (b - c) + (p + q) (b - c)^2
Solutions:
p = ((-2 q (b - c) - b (b - c) - c (c - b)) ± sqrt((2 q (b - c) + b (b - c) + c (c - b))^2 - 4 (b - c) (q^2 (b - c) + b q (b - c) - c q (b - c))))/(2 (b - c)) (b!=c)
Geometric figure:
line
Alternate forms:
(b - c) (p + q) (b - c + p + q)
b (b (p + q) + p (-2 c + p + 2 q) + q (q - 2 c)) + p (c^2 - c p - 2 c q) + q (c^2 - c q)
b (b (p + q) + c (-2 p - 2 q) + p (p + 2 q) + q^2) + c (c (p + q) + p (-p - 2 q) - q^2)
Expanded form:
b^2 p + b^2 q - 2 b c p - 2 b c q + b p^2 + 2 b p q + b q^2 + c^2 p + c^2 q - c p^2 - 2 c p q - c q^2
Polynomial discriminant:
Δ_p = b^4 - 4 b^3 c + 6 b^2 c^2 - 4 b c^3 + c^4
Derivative:
d/dp((p + q)^2 (b - c) + (p + q) (b - c)^2) = (b - c) ((b - c) + 2 (p + q))
Indefinite integral:
integral((b - c)^2 (p + q) + (b - c) (p + q)^2) dp = (b - c) (1/2 p^2 (b - c + 2 q) + p q (b - c + q) + p^3/3) + constant