Quant Algebra Formulas/Identities
Algebra may seem difficult to most of you, but we will help you make it your trump card! Quickly go through the Basic algebra formulas to brace yourselves for the questions that follow.
BASIC ALGEBRA IDENTITIES
(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 + b2 – ab)
a3 – b3 = (a – b) (a2 + b2 + ab)
(a + b + c)2 = a2 + b2 + c2 + 2 (ab + bc + ca)
(a + b + c)3 = a3 + b3 + c3 + 3(a + b) (b + c) (c + a)
a3 + b3 + c3 – 3abc = (a + b + c) (a2 + b2 + c2 – ab – bc – ca)
= ½ (a + b + c) [(a – b)2 + (b – c)2 + (c – a)2]
(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 + b2 – ab)
a3 – b3 = (a – b) (a2 + b2 + ab)
(a + b + c)2 = a2 + b2 + c2 + 2 (ab + bc + ca)
(a + b + c)3 = a3 + b3 + c3 + 3(a + b) (b + c) (c + a)
a3 + b3 + c3 – 3abc = (a + b + c) (a2 + b2 + c2 – ab – bc – ca)
= ½ (a + b + c) [(a – b)2 + (b – c)2 + (c – a)2]
Now that you have revised the important algebra identities, try your hands at the following questions before we give you the cheat sheet. We have picked these questions from the previous year papers.
Directions: What should come in place of ‘?’ in the following questions?
abc
a + b + c
ab + bc + ca
3
Commonly Used Detailed Method
⇒ bc + a (b + c) =?
∴ Answer = bc + ab + ac
Option – 3
∴ Answer = bc + ab + ac
Option – 3
Lengthy isn’t it? Want to know how you can solve this question in a few seconds? Read further to know the short trick.
Quant Algebra Short Trick – Know How to Solve in Seconds?
Time plays a very important part in any exam and using the above conventional method would easily eat up your 5-10 mins. Learn how you can solve this difficult algebra question in just a few seconds.
The above equation is a perfect example of homogeneous expressions because all the expressions have the same degree.
Degree of overall expression = 2
Now if you check the degrees of the options:
abc: Degree = 3
a + b + c: Degree = 1
ab + bc + ca: Degree = 2
3: Degree = 0
∴ option 3 i.e. ab + bc + ca is the right answer.
Note
1) While calculating the degree of expression, keep in mind that we add the values of exponents if the variables are multiplied, we subtract the values if the values are divided and if the variables are added or subtracted then the highest degree is taken.
2) A degree is the highest power of the expression.
How to find the degree of an expression?
ExpressionCorresponding DegreeExplanationa33Value of exponentb or c1Value of exponent(b + c), (a– b) or (a-c)1Highest Degreea3 (b + c)3 + 1 = 4Values are added because they are multiplied(a – b) (a-c)1 + 1 = 2Values are added because they are multiplied.
4 – 2 = 2Values are subtracted because they are dividedabc1 + 1 + 1 = 3Values are added because they are multiplied.a + b + c1Highest Degreeab + bc + ca1 + 1 = 2Values are added firstly because they are multiplied,
and the highest value is taken.30Variable is having 0 exponents.
4 – 2 = 2Values are subtracted because they are dividedabc1 + 1 + 1 = 3Values are added because they are multiplied.a + b + c1Highest Degreeab + bc + ca1 + 1 = 2Values are added firstly because they are multiplied,and the highest value is taken.30Variable is having 0 exponents.
Quant Algebra Questions
Its time you should try out a few questions, to strengthen the concept you’ve just read. Solve the following quant Algebra questions
Q.1 
1) a + b + c
2) 3
3) a2 + b2 + c2
4) abc
Check Answer & Solution Here
The above equation is a perfect example of homogeneous expressions because all the expressions have the same degree.
Degree of overall expression = 1
Checking options:
Degree = 1
Degree = 0
Degree = 2
Degree = 3
∴ option 1 i.e. a + b + c is the right answer.
Q.2 (bc + ca + ab)3 – b3c3 – c3a3 – a3b3 = ?
1) 3abc (a + b) (b + c) (c + a)
2) (a + b) (b + c) (c + a)
3) (a – b) (b – c)(c – a)
4) 24abc
Check Answer & Solution Here
The above equation is a perfect example of homogeneous expressions because all the expressions have the same degree.
Degree of (bc + ca + ab)3 = 2 × 3 = 6
Degree of b3c3 = 3 + 3 = 6
Degree of c3a3 = 3 + 3 = 6
Degree of a3b3 = 3 + 3 = 6
Degree of overall expression = 6
Checking options:
Degree = 6
Degree = 3
Degree = 3
Degree = 3
∴ option 1 i.e. 3abc (a + b) (b + c) (c + a) is the right answer.
Q3. 
1) 1
2) x/y
3) (xyzw)m
4) (xyzw)m/2
Check Answer & Solution Here
Checking options:
Degree = 0
Degree = 0
Degree = 4m
Degree = 2m
∴ option 4 i.e. (xyzw)m/2 is the right answer.
Q4. (x + y + z)3 – (x + y – z)3 – (y + z – x)3 – (z + x – y)3 = ?
1) 8(x + y + z)
2) 24xyz
3) 12
4) 24
Check Answer & Solution Here
The above equation is a perfect example of homogeneous expressions because all the expressions have the same degree.
Degree of (x + y + z)3= 3
Degree of (x + y – z)3 = 3
Degree of (y + z – x)3 = 3
Degree of (z + x – y)3= 3
Degree of overall expression = 3
Checking options:
Degree = 1
Degree = 3
Degree = 0
Degree = 0
∴ option 2 i.e. 24xyz is the right answer.
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