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A Plus B whole cube formula pdf

A+B Whole Cube

A Plus B whole cube formula is an algebraic identity. (a + b)3 = a3 + 3ab(a+b) + b3 used to find the cube of binomial.

  • The a plus b whole cube is equal to the a cubed plus b cubed plus three times the product of a , b and sum of a plus b

How to derive A Plus B whole cube

Lets understand this (A+B)3 Formula in details. this formula is the cube of the sum of two variables or terms.

  • (a + b)3 = (a + b)(a + b)(a + b)
  • = (a2 + 2ab + b2)(a + b)
  • = a3 + a2b + 2a2b + 2ab2 + ab2 + b3 
  • = a3 + 3a2b + 3ab2 + b3 
  • = a3 + 3ab(a+b) + b3 
  • Therefore, (a + b)^3 formula is:
  • (a + b)3 = a3 + 3a2b + 3ab2 + b3

List of Some important Algebraic formula

  • (a + b)3 = a3 + b3 + 3ab (a + b)
  • (a – b)3 = a3 – b3 – 3ab (a – b)
  • ( a − b ) 3 = a 3 − b 3 − 3 a b ( a − b )
  • ( a − b ) 3 = a 3 − b 3 − 3 a b ( a − b )
  • ⟹ ( a − b ) 3 = a 3 − b 3 − 3 a 2 b + 3 a b 2.
  • ⟹ ( a − b ) 3 = a 3 − b 3 − 3 a b ( a − b )
  • (a + b)2 = a2 + 2ab + b2
  • (a – b)2 = a2 – 2ab + b2
  • (a + b) (a – b) = a2 – b2
  • (x + a) (x + b) = x2 + (a + b) x + ab
  • (x + a) (x – b) = x2 + (a – b) x – ab
  • (x – a) (x + b) = x2 + (b – a) x – ab
  • (x – a) (x – b) = x2 – (a + b) x + ab
  • (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
  • (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
  • (x + y + z)2 = x2 + y2 + z2 + 2xy +2yz + 2xz
  • (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
  • (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
  • (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
  • x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz -xz)
  • x+ y2 = 1212 [(x + y)2 + (x – y)2]
  • (x + a) (x + b) (x + c) = x+ (a + b + c)x2 + (ab + bc + ca)x + abc
  • x3 + y3 = (x + y) (x– xy + y2)
  • x3 – y3 = (x – y) (x+ xy + y2)
  • x2 + y2 + z2 – xy – yz – zx = 1212 [(x – y)2 + (y – z)2 + (z – x)2]

Solved examples using A+B Whole Cube formula

Now you can understand this (A+B)3 formula in detail by solving some good examples

Example 1: Solve the following expression using suitable algebraic identity: (2p + 3q)3

Solution: Using (a + b)3 Formula, (a + b)3 = a3 + 3a2b + 3ab2 + b3 Here in given question, we can assume a = 2p and b = 3q, now put these variables in formula
= (2p)3 + 3 × (2p)2 × 3q + 3 × (2p) × (3q)2 + (3q)3
= 8p3 + 36p2q + 54pq2 + 27q3

Example 2: Find the value of p3 + 8q3 if p + 2q = 6 and pq = 2.  

Solution:   We have to find: p3 + 8q3

In the question, given terms are : p + 2q = 6 and pq = 2. Now to solve this question we will use (a + b)3 A plus B whole cube formula, (a + b)3 = a3 + 3a2b + 3ab2 + b3 In this question Here, a = p; b = 2q
Therefore,
(p + 2q)3 = p3 + 3 × p2 × (2q) + 3 × p × (2q)2 + (2q)3
(p + 2q)3 = p3 + 6p2q + 12pq2 + 8q3
63 = p3 + 6pq(p + 2q) + 8q3
216 = p3 + 6 × 2 × 6 + 8q3
 p3 + 8q3 = 144

FAQs on A Plus B whole cube formula

What Is the Expansion of (a + b)3 Formula?

(a + b)3 = a3 + 3ab(a+b) + b3

What Is the (a + b)3 Formula in Algebra?

(a + b)3 = a3 + 3ab(a+b) + b3

What is (a+b)^3 formula ?

(a + b)3 = a3 + b3 + 3ab(a + b)

What is A +B 3?

(a + b)3 = a3 + b3 + 3ab(a + b)

What is the formula of A plus B whole cube?

(a + b)3 = a3 + 3ab(a+b) + b3 The a plus b whole cube is equal to the a cubed plus b cubed plus three times the product of a , b and sum of a plus b

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