How Do You Factor, To Reach , ? Please Help

How do you factor(a+b)^{3} to reach a^{3} +3a^{2}b+3ab^{2}+b^{3}? Please help

 

Answer:

Easily get the product of (a + b)³ or (a + b)(a + b)(a + b) by using the Cube of a Binomial Formula.

Formula (F stands for first term while L stands for last term):

(F + L)³ = F³ + (3)(F)²(L) + (3)(F)(L)² + L³

  • Cube the first term.
  • Multiply 3 to the square of the first term then multiply again with the last term.
  • Multiply 3 to the first term then multiply again to the square of the last term.
  • Cube the last term.

Example:

(2a + 4b)³ =  (2a)³ + (3)(2a)²(4b) + (3)(2a)(4b)² + (4b)³

= 8a³ + (3)(4a²)(4b) + (3)(2a)(16b²) + 64b³

= 8a³ + (12a²)(4b) + (6a)(16b²) + 64b³

= 8a³ + 48a²b + 96ab² + 64b³


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