Sum of cubes:
We can factorize an expression involving sum of cubes using the following formula.
a3 + b3 = (a+b) (a2 – ab + b2)
Example 1:
Factorize the expression x3 + 8.
Solution:
x3 + 8 = x3 +23
Here a=x and b= 2.
Using the above formula,
x3 +23 = (x+2) (x2 – x*2 + 22) = (x+2) (x2 – 2x + 4)
Example 2:
Factorize the expression 3x3 + 81.
Solution:
3x3 + 81 = 3(x3 + 27) = 3(x3+33) = 3(x+3) (x2 – 3x + 9) (By using the above formula).
Difference of cubes:
We can factorize an expression involving difference of cubes using the following formula.
a3 – b3 = (a-b) (a2 + ab + b2)
Example 1:
Factorize the expression x3 – 8.
Solution:
x3 – 8 = x3 – 23
Here a=x and b= 2.
Using the above formula,
x3 – 23 = (x-2) (x2 + x*2 + 22) = (x-2) (x2 + 2x + 4)
Example 2:
Factorize the expression 3x3 – 81.
Solution:
3x3 – 81 = 3(x3 – 27) = 3(x3-33) = 3(x-3) (x2 + 3x + 9) (By using the above formula).
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