Question 505745

{{{4y^3+12y^2-y-3}}} Start with the given expression



{{{(4y^3+12y^2)+(-y-3)}}} Group the terms in two pairs



{{{4y^2(y+3)-1(y+3)}}} Factor out the GCF {{{4y^2}}} out of the first group. Factor out the GCF {{{-1}}} out of the second group



{{{(4y^2-1)(y+3)}}} Since we have the common term {{{y+3}}}, we can combine like terms



{{{(2y-1)(2y+1)(y+3)}}} Now factor {{{4y^2-1}}} to get {{{(2y-1)(2y+1)}}} (use the difference of squares formula)



So {{{4y^3+12y^2-y-3}}} factors to {{{(2y-1)(2y+1)(y+3)}}}



In other words, {{{4y^3+12y^2-y-3=(2y-1)(2y+1)(y+3)}}}


Let me know if you need more help or if you need me to explain a step in more detail.
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Thanks,


Jim