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)
• x² + y² = 1212 [(x + y)² + (x – y)²]
• (x + a) (x + b) (x + c) = x³ + (a + b + c)x² + (ab + bc + ca)x + abc
• x³ + y³ = (x + y) (x² – xy + y²)
• x³ – y³ = (x – y) (x² + 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

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