could someone help me with math?

Question

Perform the indicated operations.

(3x+5)^3

 

i know how to set it up (3x+5) (3x+5) (3x+5) however i don't know how to distrubute three times. i usually just do two 

Answer 1

There are three methods. 

 

You have probably learned to multiply by using FOIL. So, lets assume you have done that already, and you are now looking at  (9x² + 30x + 25) (3x+5)

 

You can multiply through by your first term 9x², add those results to multiplying through by 30x and add those to multiplying through by 25

 

(27x³ + 45x²) + (90x² + 150x) + (75x + 125)

 

now combine like terms

 

27x³ + (45x² + 90x²) + (150x + 75x) + 125

27x³ + 135x² + 225x +125

 

 

This is how you should start multiplying higher order polynomials.

 

The second method you will grow into is to do the grouping  of cubic, quadratic, linear, and constant terms as you multiply them

 

(9x²)(3x) + (9x²⁾(5) + (30x)(3x) + (30x)(5) + 25(3x) + (25)(3x) + (25)(5)

 

 

The third way is called Pascal's Triangle  The coefficients of (a+b)³ are 1,3,3,1

 

(1)(3x)³ + (3)(3x)²(5) + (3)(3x)(5)² + (5)³