Please solve 49 th and 50th question plaza will surely mark branliest ,
Answers
Answer:
Well 50th was a bit tricky one it's actually conditional!
Answer:
Step-by-step explanation:
49) x³ - 64y³ - 12x²y + 48xy²
= (x)³ - 3(x)²(4y) + 3(x)(4y)² - (4y)³
this of form a³ - 3a²b + 3ab² - b³ which is equal to (a - b)³
= (x - 4y)³
50) (25)³ - (20)³ - (5)³
if we consider three terms a , b, c as a = 25, b = 20 and c = 5.
we need to find value of a³ - b³ - c³
a³ - b³ - c³ = (a³ - b³) - c³
=> (a - b)³ + 3ab(a -b) - c³ (∵ a³ - b³ = (a - b)³ + 3ab (a-b) )
=> (a - b)³ - c³ + 3ab(a -b) ( just changed positions of c³ and 3ab(a-b))
=> (a - b - c)³ + 3(a-b)(c)(a-b-c) + 3ab(a-b) (∵ a³ - b³ = (a - b)³ + 3ab (a-b) )
=> (a-b-c)³ + 3(a-b)(ac - bc - c² + ab)
=> (a-b-c) ³ + 3(a-b)[c(a-c) + b(a-c)]
=> (a-b-c) ³ + 3(a-b)[(a-c)(b+c)]
=> (a-b-c) ³ + 3(a-b)(a-c)(b+c)
=> (a-b-c) ³ - 3(a-b)(b+c)(c-a) (∵ c - a = - (a-c))
So now substitute the values of a, b and c here
=> (25 - 20 -5)³ - 3(25 - 20)(20+5)(5 - 25)
=> 0 - 3*5*25*(-20)
=> 3 * 125 * 20 = 7500.