Factoring?

Question

How would you factor these?

c^4-2c^2+1

(y-3)^3 - (y-3)^2

Answer 1

Hi,

(c² - 1)(c² - 1) = (c - 1)²(c + 1)²

(y - 3)³ - (y - 3)² = (y - 3)²(y - 3 - 1) = (y - 3)²(y - 4)

I hope that helps!! :-)

Answer 2

c^4 - 2c^2 + 1
The coefficient of c^4 is 1 and the constant of the equation is 1. The product of these two factors is 1. We find factors of 1 such that when added together will give us the central coefficient of -2. That is -1, -1. We use this to break up the central expression and get:
c^4 - c^2 - c^2 +1.
We now group two terms at a time factoring out the common terms:
c^2(c^2-1) -1(c^2 - 1)
Since c^2 - 1 is common in the parenthesis we factor it out and have:
(c^2 - 1)(c^2 - 1) = (c^2 - 1)^2.


(y - 3)^3 - (y - 3)^2
Factoring out the common term (y - 3)^2 we have:
(y - 3)^2[y - 3 - 1] = (y - 3)^2(y - 4)
So the final factors are:
(y - 3)^2(y - 4).

Answer 3

[15]
c^4-2c^2+1
=(c^2)^2-2*c^2*1+(1)^2
=(c^2-1)^2
={(c+1)(c-1)}^2

(y-3)^3-(y-3)^2
=(y-3)^2{(y-3)-1}
=(y-3)^2(y-3-1)
=(y-3)^2 (y-4)
there is an easier way to understand the above factoring
(y-3)^3-(y-3)^2
substituting y-3 by a ,the expression becomes
a^3-a^2
=a^2(a-1)
Putting back the value of a ,we get
(y-3)^2 (y-3-1)
=(y-4)(y-3)^2

Answer 4

(c² - 1)(c² - 1)
(c - 1)(c + 1)(c - 1)(c + 1)
(c - 1)² (c + 1)²

(y - 3)² (y - 3 - 1)
(y - 3)² (y - 4)