Cube difference Trick|How to Solve A³-B³ , if we know the Difference between A & B ?

 Cube difference Trick

How to Solve A³-B³ , if we know the Difference between A & B ?

Formula:

If A - B =D

Then A³ - B³ = Difference ×3AB + (Difference)³

If A - B = 1,

Then A³ - B³ = 3AB + 1

Example:

Find the value of,

(56)³ - (58)³ = ?

Answer:

Here A = 58 & B = 56

A - B = 2

As we know A³ - B³ = Diff.×3AB+(Diff.)³

= 2 × 3(58×56) + (2)³

=19488 + 8 

=19496

Find the value of 

(36)³ - (35)³

Answer:

Here A - B = 1

Hence,

A³ - B³ = 3AB+1

= 3 × (36×35) + 1

=3780 + 1

=3781

Explanation:

Let's consider A = a+1 & B=a

Now A³ - B³

(a + 1)³ - (a)³

= a³ + 1³ +3.a.1(a + 1) - a³

= a³ + 1 + 3a² + 3a - a³

= 1 + 3a(a + 1)

= 3AB + 1.               ,  As A - B = a+1 - a = 1

If A = a+2. &  B = a

(a +2)³ - a³

= a³ + 8 + 3a.2(a +2) - a³

= 8 + 6a(a + 2)

= 8+ 2 × 3a(a+2)

= 2 × 3AB + 2³ = Diff. × 3AB + (Diff.)³

(Proved)

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