how to do this kind of problem ?

Question

can some one explain the steps how to answer this problem I have a very hard time under standing this problem

(x2+x+3)(x3-x2-+4)

Answer 1

If you are seeing this sort of equation, then you are probably familiar with the FOIL process: distribute First, Outer, Inner, Last.

This is essentially the same process, the only difference is that you have three in each parentheses instead of two:

To begin the distributing method, let me help by giving you a visualization cue:

x²(x³ - x² + 4) + x(x³ - x² + 4) +3(x³ - x² + 4)

 

Does that help you visualize what's going on? We've distributed the first parenthesis to the second set.

Now it's just a matter of distributing what's outside to what's inside. I'll keep the parenthesis sets to help contain what's going on where:

(x⁵ - x⁴ + 4x²) + (x⁴ - x³ + 4x) + (3x³ - 3x² + 12)

 

Now it's just a matter of adding/subtracting like terms:

x⁵ = x⁵

-x⁴ + x⁴ = 0

-x³ + 3x³ = 2x³

4x² -3x² = x²

4x = 4x

12 = 12

 

That gives us the final answer of:

x⁵ + 2x³ + x² + 4x + 12

Answer 2

We have here two factors.  Lets say that  (x² + x + 3)  is the GCF of the expression.  Then we can write the expression as

 

x³(x² + x + 3) - x²(x² + x + 3) - 4(x² + x + 3)

 

 

Distribute and combine any like terms.  That's all there is to it.