SOLUTION: Hello. I was hoping you could please help me with this problem. I have to factor completely, and if prime, say so. a. 40x^3 - 64x^2y b. 13-14y + y^2 c. 9x^2- 30 +

a.   

The largest whole number that will divide into both  and  is .
So we can take out an .

The largest power of x that will divide into both  and 
is .

So we can take out 




b.   

Write it in descending order:



Think of two positive integers which multiply to give 13,
and when added give 14. 

[If the red sign had been - I would have said "subtracted"]

They are 13 and 1

Write this

(x   13)(x   1)



Since the green sign is -, put a minus before the large of those
two numbers which is 13:

(x - 13)(x   1)

Since the red sign is negative put the OPPOSITE sign before the 1
that you put before the 13.

(x - 13)(x + 1)

[If the red sign had been + I would have said "SAME"]



c.   

This is a special case where the first term and the last term are both
perfect squares.  the  has square root  and the 
has square root .  Multiply these square roots together, getting ,
and then double that, getting .  Since this is the absolute value
of the middle term, the trinomial is a perfect square, so write

(3x   5)²

and the sign that goes between them is the same sign as the middle term:

(3x - 5)²

Edwin