(3x-1)^7, then addition of all cofactors is =?

Question :(3x-1)⁷, then addition of all cofactors is =? if cofactors are A7,A6,A5,A4,A3,A2,A1,A0

Solution

1.       3x-1=3x-1

2.       (3x-1)²=9x²−6x+1

3.       (3x-1)³=27x³−27x²+9x−1

4.       (3x-1)⁴=81x⁴−108x³+54x²−12x+1

5.       (3x-1)⁵ =243x⁵−405x⁴+270x³−90x²+15x−1

6.       (3x-1)⁶ =729x⁶−1458x⁵+1215x⁴−540x³+135x²−18x+1

7.       (3x-1)⁷ =2187x⁷−5103x⁶+5103x⁵−2835x⁴+945x³−189x²+21x−1
  Key to answer :Addition of An,A(n-1),A(n-2).............A0=2^n

Algebra	Cofactors for the algebraic expression (3x-1)7
	A7		A6	A5	A4	A3		A2	A1	A0	Total
3x-1									3	-1	2
(3x-1)2								9	-6	1	4
(3x-1)3							27	-27	9	-1	8
(3x-1)4					81		-108	54	-12	1	16
(3x-1)5				243	-405		270	-90	15	-1	32
(3x-1)6		729		-1458	1215		-540	135	-18	1	64
(3x-1)7	2187	-5103		5103	-2835		945	-189	21	-1	128

If the polynomial 16X4—24X3+41X2-mx+16 is a perfect square, then find the value of m (A)12 (B) -12 (C) 24 (D) -24

If the polynomial 16X⁴—24X³+41X²-mx+16 is a perfect square, then find the value of m

(A)12 (B) -12 (C) 24 (D) -24

Solution :Let find it using division method to find square root of an algebraic expression

A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it?

A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it?

(A) 30 days

(B) 35 days

(C) 40 days

(D) None of these

Solution:

1.  Let B does the work in B days, then B in 1 day will do 1/B part of work

2.  A takes three-fourth of working days of B to do half of work done by B, therefore A in 3/4XB days will do 1/2 work, then in 1 day A would do 1/2÷3/4XB=2/3B part of work

3.  A and B together in 1 day will do =1/B+2/3B=5/3B part of work

4.  As given, A and B do 1 work in 18days, then A and B together in 1 day will do 1/18 part of the work

5.  Therefore, looking at step 3 and 4 ,5/3B=1/18, THEN B=30DAYS (Answer)

The ratio of the incomes of P and Q is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves 1600, then the income of P is

The ratio of the incomes of P and Q is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves 1600, then the income of P is=?

Solution :

1.       Let income of P and Q are PI and QI,then PI/QI=5/4,THEN QI=4/5.PI

2.       Let expenditure of P and Q are PE and QE,then PE/QE=3/2 ,THEN PE=3/2.QE

3.       Saving =Income -expenditure

4.       Saving of P is PI-PE=1600 AND QI-QE=1600, then QE=QI-1600

5.       We need income of P=PI

   From above (4) we know PI-PE=1600, Then replacing PE value from above (2), PI-3/2XQE=1600, then replacing QE from above (4), PI-3/2(QI-1600) =1600, then replacing QI from above (1), PI-3/2(4PI/5-1600) =1600, then PI-12PI/10+2400=1600, then -2PI/10=-800, then 2PI=8000, then PI=4000(ANSWER).