Formulas for Cube

In this topic formulas for cube we are going to discuss about formulas which are being used to expand the terms like in the form (a ³ - 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.

Problems on formulas for cube.

Question 1 :

Expand ((5x)³ - 2 ³))

Solution:

Here the question is in the form of (a ³ - b ³). Instead of a we have "5x" and instead of b we have "2" . Now we need to apply the formula (a-b)(a² + ab + b²) and we need to apply those values instead of a and b


(5x)³ - 2 ³   = (5x - 2) ((5x)² + 5x(2) + 2 ² )

                 = (5x-2) (5²x² + 5x(2) + 2²)

                 = (5x-2) (25x² + 10x + 2²)


 The formula for cube

                   (a ³ - b ³) = (a-b)(a² + ab + b²)

is  called sum of cubes.  This is used to solve many algebraic expressions. If the binomial in the left side has subtraction sign, then the binomial in the right hand side must have negative sign, and the trinomial must have positive sign for the term which involves both the variables.

        Let us see another example for formula for cube.



Question 2 :

Expand (x³ - 1 ³)

Solution:

Here the question is in the form of (a ³ - b ³). Instead of a we have "x" and instead of b we have "1" . Now we need to apply the formula (a-b)(a² + ab + b²) and we need to apply those values instead of a and b


x³ - 1 ³   = (x - 1) (x² + x(1) + 1 ² )

             = (x-1) (x² + x + 1) 


 Students can practice the above problems and can do the worksheets given in the below link.  They can verify their solutions with the solutions given. Still if you are having any doubt you can contact us through mail, we will help you to clear your doubts.

Formulas for cube to algebraic identities

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