A MINUS B  WHOLE CUBE FORMULA

On this webpage a minus b whole cube formula, that is (a - b)³ we are going to see some example problems based on this formula.

What is Algebraic identity?

An identity is an equality that remains true regardless of the values of any variables that appear within it.

Now let us see a minus b whole cube formula

Question 1 :

Expand (x - 1)³

Solution:

Here the question is in the form of (a-b)³.  Instead of 'a' we have "x"and instead of 'b' we have "1" . Now we need to apply the formula a³- 3a² b + 3ab² - b³ and we need to apply those values instead of a and b 

(x - 1)³  = (x)³ - 3 (x)²(1)+ 3 (x)(1)² - (1)³

               = x³- 3 (x²)(1) + 3(x)(1) - 1

               = x³ - 3 x ² + 3 x - 1 


Now let us see another example problem using a minus b whole cube formula

Question 2: 

Expand (2a -3)³

Solution:

Here the question is in the form of (a-b)³.  Instead of 'a' we have "2a²"and instead of 'b' we have "3" . Now we need to apply the formula a³- 3a² b + 3ab² - b³ and we need to apply those values instead of a and b 

(2a²- 3)³  = (2a²)³ - 3 (2a²)²(3)+ 3 (2a²)(3)² - (3)³

               = 8a⁶- 3(4)(3) a⁴ + 3(2)(9)a² - 27

               = 8a⁶- 36 a⁴ + 54a² - 27


Question 3:

(2b-3d)³

Solution:

Here the question is in the form of (a-b)³.  Instead of 'a' we have "2b"and instead of 'b' we have "3d" . Now we need to apply the formula a³- 3a² b + 3ab² - b³ and we need to apply those values instead of a and b 

(2b- 3d)³  = (2b)³ - 3 (2b)²(3d)+ 3 (2b)(3d)² - (3d)³

               = 8b³ - 3(4)3b²d +3(2)(9)bd² - 27d³

               = 8b³ - 36b²d +54 bd² - 27 d³


Question 4: 

Find the value of 98³

Solution:

98³ = (100 - 2)³

Instead of multiplying 98 three times to get the value of 98³,we can use a plus b whole cube formula.Here the question is in the form of (a- b)³. Instead of a we have"100" and instead of b we have "2".

(a - b)³ = (a³ - b³) - 3 a b (a - b)

(100 - 2)³ = (100)³ - 2³ - 3 (100) (2) (100 - 2)

                   = 1000000 - 8 - 600 (98)

               = 1000000 - 8 - 58800

               = 941192






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(a + b)² = a² + 2 ab + b²

(a - b)² = a² - 2 ab + b²

a² - b² = (a + b) (a - b)

(x+a)(x+b)=x²+(a+b)x+ab

(a+b)³=a³+3a²b+3ab²+b³

(a-b)³=a³-3a²b+3ab²-b³

(a³+b³)= (a+b)(a²-ab+b²)

(a³-b³)=(a-b)(a²+ab+ b²)

(a+b+c)²= a²+b²+c²+2ab+2bc+2ca