Question

How do you factor $ 2{x^3} + 16 $ ?

Answer 1

Hint: First of all find the common factor from the given factor and then use the identity for the sum of the cubes of two terms and then simplify for the resultant value.

Complete step-by-step solution:
Take the given expression: $ 2{x^3} + 16 $
Take out the common multiple common from both the above terms.
 $ \Rightarrow 2({x^3} + 8) $
The above expression can be re-written as –
 $ \Rightarrow 2[{x^3} + ({2^3})] $
Using the sum of cubes identity which can be given as: $ {a^3} + {b^3} = (a + b)({a^2} - ab + {b^2}) $
 $ \Rightarrow 2[(x + 2)({x^2} - 2x + 4)] $
This is the required solution.

Additional Information: Constants are the terms with fixed value such as the numbers it can be positive or negative whereas the variables are terms which are denoted by small alphabets such as x, y, z, a, b, etc. Be careful while moving any term from one side to another. Do not be confused in square and square-root and similarly cubes and cube-root, know the concepts properly and apply accordingly.

Thus the required answer is $ 2[(x + 2)({x^2} - 2x + 4)] $ .

Note: Know the concepts of squares and cubes. Square is the number multiplied itself and cube it the number multiplied thrice. Square is the product of same number twice such as $ {n^2} = n \times n $ for Example square of $ 2 $ is $ {2^2} = 2 \times 2 $ simplified form of squared number is $ {2^2} = 2 \times 2 = 4 $ . Cube is the product of same number three times such as $ {n^3} = n \times n \times n $ for Example cube of $ 2 $ is $ {2^3} = 2 \times 2 \times 2 $ simplified form of cubed number is $ {2^3} = 2 \times 2 \times 2 = 8 $ .