SOLUTION: Could you please help me with Multiplying and Simplify x^2-x-6 16x^3-25x ------- * --------- 4x^3-5x^2 3x-9 Thanks I appreciate any help!!

Question 196229:
Could you please help me with Multiplying and Simplify
x^2-x-6 16x^3-25x
------- * ---------
4x^3-5x^2 3x-9
Thanks I appreciate any help!!!
Answer by anantha(86) (Show Source): You can put this solution on YOUR website!
sol:
step1:
------
first take the x^2-x-6
factors of x^2-x-6 are
x^2-3x+2x-6 (i.e; on multiplying we get -6 and adding we get -1)
x(x-3)+2(x-3)
(x+2)(x-3)
step2:
-----
take 4x^3-5x^2
in this x^2 is common term
this can be written as
x^2(4x-5)
step3:
------
take 16x^3-25x
here x is common term
this can be written as
x(16x^2-25)
x[(4x)^2-(5)^2]
x[(4x+5)(4x-5)] (i.e; a^2-b^2=(a+b)*(a-b))
step4:
-----
take 3x-9
here 3 is common term
this can be written as
3(x-3)
substitute all these values in the given expression
x^2-x-6 16x^3-25x
-------- * -----------
4x^3-5x^2 3x-9
(x+2)(x-3) x(4x+5)(4x-5)
---------- * ---------------
x^2(4x-5) 3(x-3)
here the canciling terms are (x-3)(4x-5)andx
after canciling the remaining terms are
(x+2)*(4x+5) 4x*x+5*x+4x*2+5*2
------------ = ------------------
3x 3x

4x^2+5x+8x+10
-------------
3x
4x^2+13x+10
-----------
3x
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