x^2(3)(2x + 1)^3(2x) + (2x + 1)^4(3x^3)

Question

Factor the expression completely. 

Answer 1

x²(3)(2x+1)³(2x)+(2x+1)^4 (3x³) To see common factors easier rewrite as follow: = 3(2x)(x²)(2x+1)³+(3x³)(2x+1)^4 simplify by multiplying terms as follow: = (6x³)(2x+1)³ +(3x³)(2x+1)^4 Now we can factor out the common terms: = (3x³)(2x+1)³[2 + (2x + 1)] Simplify: = (3x³)(2x+1)³(2x+3)

Answer 2

x²(3)(2x+1)³(2x) + (2x+1)⁴(3x³)

 

Let's multiply the simple stuff first

 

= 3x²(2x)(2x+1)³ + 3x³(2x+1)⁴

 

= 6x³(2x+1)³ + 3x³(2x+1)⁴

 

Look for the common factors...

Both are divisible by 3x³ and (2x+1)³

 

Factor our the 3x³

= 3x³[2(2x+1)³ + (2x+1)⁴]

 

Factor out (2x+1)³

= 3x³(2x+1)³[(2 + (2x+1)]

 

= (3x³)(2x+1)³(2x+3)