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.

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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