(a + b)2 = a2 + b2 + 2ab
(a - b)2 = a2 + b2 -2ab
(a2 - b2 )= (a + b) (a - b)
(a + b)3 = a3 + b3 + 3ab (a+b)
(a - b)3 = a3 – b3 -3ab (a-b)
a3 + b3 = (a+b) (a2- ab +b2)
a3- b3 = (a-b) (a2+ ab +b2)
(a+b+c)3 = a2 + b2 + c2 + 2ab +2bc + 2ca
The concept needs a better understanding and thorough reading of statements given to solve.
Let see how to figure out the number of based problems.....
Problem1: The sum of two numbers is 29 and the difference of their squares is 145. The difference between the numbers is?
Step1: Take two numbers X and Y
Step2: The sum of two numbers is 29
Step3: The difference of their squares is 145
Step4: To evaluate both the statements apply algebraic formula and put the given values here
145 = 29 (a-b)
145/29 = (a-b)
Step5: The difference of the numbers (X - Y)= 5
Problem2: The ratio between two numbers is 3:4 and their sum is 420. The greater of the two numbers is?
Step1: Take a numbers x
Step2: The ratio between two numbers is 3:4
Step3: Ratio means both the numbers are divisible with single common multiple. Let’s take it ‘x’ which will multiply with both the numbers as
Second Number = 4x
4x= 4 * 60 = 240
Step6: The second number is greater than first one
Problem3: Three fourth of one-fifth of a number is 60. The number is?
Step1: Three fourth ¾ and one fifth 1/5
Step2: ‘Of ’ designated multiplication here
Step3: A number takes it as ‘x’
3/20 * x = 60
x = 400
Step4: The number is 400
Problem4: The difference between the squares of two consecutive numbers is 35. The number are?
Step1: Consecutive numbers are numbers follow each other like 1, 2,3 ,4
Step2: Imagine two consecutive number x and (x + 1)
Step3: The difference between the squares of two numbers is 35. Square it first x2 , (x+1)2
Step4: The difference between two means subtract the smaller number from greater one i.e.
Step5: Evaluate and it comes out x=18
Step6: First number x=18
Second number is x + 1 =19
Problem5: The sum of the two numbers is twice their difference. If the one of the number is 10, the other number is?
Step1: Take two number X and Y
Step2:Take X= 10 ( Given one number)
Step3: The sum of the two numbers is twice their difference.
10 +Y = 20 -2Y
Step4: Other number is 10/3 or take in mixed fraction as 3 1/3
Problem6: The number whose fifth part is increased by 5 is equal to its fourth part diminished by 5. The number is?
Step1: Take a number X
Step2: Fifth part of number is 1/5 of x and fourth part of number is 1/4 of x
Step3: The number whose fifth part is increased by 5 is equal to its fourth part diminished by 5
Step4: Evaluate it
10 = x/4 – x/5
Post on the Higher level difficulty in Numbers is coming soon.......
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