SOLUTION: Hello. Could you please help me? I have to factor these completely, and if prime, say so. Can you please show me how? Thank you so much. e. 125r^3

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Question 327860: Hello. Could you please help me?
I have to factor these completely, and if prime, say so.
Can you please show me how? Thank you so much.
e. 125r^3 - 8s^3
f. 5c^2 + 2c - 3
g. 16u^4 - v^4
thank you.

Answer by romerr1(7) (Show Source):
You can put this solution on YOUR website!
e.125^3-8s^3
Difference of two cubes formula: a^3-b^3=(a-b)(a^2+ab+b^2)
125^3-8s^3= (5-2s)(25+10s+4s^2)

f.5c^2+2c-3
This trinomial is of the form ax^2+bx+c with a=5,b=2,and c= -3.
Find two numbers whose product is a*c or 5*-3= -15, and whose sum is b or 2.
The numbers are 5 and -3.
Write +2c as +5c-3c
= 5c^2+5c-3c-3
Now factor by grouping
= 5c(c+1)-3(c+1)
= (c+1)(5c-3)

g.16u^4-v^4
=(4u^2-v^2)(4u^2+v^2)
=(2u-v)(2u+v)(4u^2+v^2)

SOLUTION: Hello. Could you please help me? I have to factor these completely, and if prime, say so. Can you please show me how? Thank you so much. e. 125r^3 - 8s^3 f. 5c^2 + 2c -