A PLUS B WHOLE CUBE FORMULA

On this webpage a plus 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?

Now let us see the

a plus b whole cube formula

Question 1 :

Expand (2x + 3) ³

Solution:

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

(2x + 3)³  = (2 x)³ + 3 (2 x)²(3)+ 3 (2x) (3)² + (3)³

               = 2³x³ + 3 (4x²)(3) + 3(2x)(9) + 27

               = 8 x³ + 36 x ² + 54 x + 27


Question 2 :

Expand (x + 4) 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 "4" . Now we need to apply the formula a³ + 3a² b + 3ab² + b ³ and we need to apply those values instead of a and b

(x + 4)³   = (x)³ + 3 (x)²(4)+ 3 (x)(4)² + (4)³

               = x³ + 3 (x²)(4) + 3(x)(16) + 64

               = x³ + 12 x ² + 48 x + 64 


Question 3: 

Expand (p+2q)³

Solution:

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

(p + 2q)³   = (p)³ + 3 (p)²(2q)+ 3 (p)(2q)² + (2q)³ 

               = p³ + 3 (p²)(2q) + 3(p)(4q²) + 8q³

               = p³ + 6p ²q + 12pq² + 8q³ 


Question 4: 

Find the value of 102³

Solution:

102³ = (100 + 2)³

Instead of multiplying 102 three times to get the value of 102³,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 (102)

                 = 1000008 + 61200

                 = 1061208   



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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