In this topic formula for cube which comes under algebra, we are going to discuss about two 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.

Examples on formula for cube:

Question 1 :

Expand x³ + 2 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 **"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

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

= (x+3) (x² - 3x + 9)

There fore the expansion of x³ + 2 ³ is (x+3) (x² - 3x + 9)

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 addition sign, then the binomial in the right hand side must have addition sign, and the trinomial must have negative sign for the term which involves both the variables.

Let us see another example for formula for cubes.

Question 2 :

Expand (3x)³ + 4 ³

**Solution:**

Here the question is in the form of (a ³ + b ³). Instead of a we have **"3x" ** and instead of b we have **"4" **. Now we need to apply the formula **
(a+b)(a² - ab + b²) ** and we need to apply those values instead of a and b

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

= (3x+4) ((3 ²x² - (3x)(4) + 4²)

= (3x+4) (9x² - 12x + 16)

There fore the expansion of (3x)³ + 4 ³ is (3x+4) (9x² - 12x + 16)

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.

Formula for cube to algebraic identities

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