Cube formula in Algebra





In this topic cube formula in algebra we are going to discuss about two formulas which are being used to expand the terms like in the form (a + b) ³. We are going to see some of the example problem.After getting clear of using this you can try the worksheet also.

We have given this worksheet for the purpose of making practice.If you practice this worksheets it will become easy to face problems in the topic algebra.We will use these formulas in most of the problem

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   = (2x)³ + 3 (2x)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 

Students can go through the examples discussed above in this page 'Cube formula in algebra' and try to do on their own. If you are having any doubt you can contact us through mail, we will help you to clear your doubts.



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