Question

How would you simplify this complex expression:
(12) (x+7)^3 (3x+1)^3 + (3)(x+7)^2 (3x+1)^4
~This is my 3rd time to post this and I'm not so much needing the answer (I've been given that already) but I'm trying to figure out how the actual process works (as in step-by-step). Thanks!

Answer 1

PEDMAS
Parenthesis Exponents Divide Multiply Add Subtract. Work the equation in that order.

Answer 2

Thanks~ but I'm not needing to work the equation..I'm just supposed to simplify it. The answer is 3(x+7)^2(3x+1)^3(7x+29). I just need to know how the whole simplification process works in between.

Answer 3

Look for common factors, starting with constants 12 and 3. Factor out the common factor 3. Look at the powers of x + 7. #hird power and second power. Common factor(x + 7)^2 gets factored out. Powers of (3x + 1): 3rd and 4th powers. Factor out (3x + 1)^3. Result:
\[3(x + 7)^{2}(3x + 1)^{3}[4(x + 7) + (3x + 1)]\]

Answer 4

Last thing: simplify the quantity in [ ]'s.

Answer 5

Look at common factors
3 goes into 12 so we can factor a 3 out of both terms
(x+7)^3 and (x+7)^2
i have 3 (x+7)'s in 1st terms but 2 in 2nd term
that means we can factor out 2 of them or an (x+7)^2
there are 3 (3x+1)'s in 1st term and 4 in 2nd term
most i can factor out of both is 3 or an (3x+1)^3
When you factor, divide each term by whatever you are factoring out
so factor out a 3(x+7)^2(3x+1)^3
whats left over in 1st term is 4(x+7)
whats left over in 2nd term is (3x+1)
=> 3(x+7)^2(3x+1)^3[4(x+7) +(3x+1)]
distribute and combine like terms
=>3(x+7)^2(3x+1)^3(7x + 29)

Answer 6

Wow!! Thank y'all so incredibly much!! :) I didn't even think about simplifying it that way but that makes perfect sense. Thank you!

Answer 7

:)