Question 150454
{{{(2b +3)(5b-1)-(b + 2)^2}}} Start with the given expression.



{{{(10b^2+13b-3)-(b + 2)^2}}} FOIL {{{(2b +3)(5b-1)}}} to get {{{(2b +3)(5b-1)=10b^2-2b+15b-3=10b^2+13b-3}}}



{{{(10b^2+13b-3)-(b + 2)(b + 2)}}} Expand {{{(b + 2)^2}}} to get {{{(b + 2)(b + 2)}}}



{{{(10b^2+13b-3)-(b^2+4b+4)}}} FOIL {{{(b + 2)(b + 2)}}} to get {{{(b + 2)(b + 2)=b^2+2b+2b+4=b^2+4b+4}}}



{{{10b^2+13b-3-b^2-4b-4)}}} Distribute the negative. Think of {{{-(b^2+4b+4)}}} as {{{-1(b^2+4b+4)}}}



{{{(10b^2-b^2)+(13b-4b)+(-3-4)}}} Group like terms. Make sure that each group is separated by a "+" sign.



{{{(9b^2)+(13b-4b)+(-3-4)}}} Subtract {{{b^2}}} from {{{10b^2}}} to get {{{9b^2}}}



{{{(9b^2)+(9b)+(-3-4)}}} Subtract {{{4b}}} from {{{13b}}} to get {{{9b}}}



{{{(9b^2)+(9b)+(-7)}}} Subtract {{{4}}} from {{{-3}}} to get {{{-7}}}



{{{9b^2+9b-7}}} Remove the parenthesis.



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Answer:



So {{{(2b +3)(5b-1)-(b + 2)^2}}} simplifies to {{{9b^2+9b-7}}}


In other words,  {{{(2b +3)(5b-1)-(b + 2)^2=9b^2+9b-7}}}