Given: #5(x + 3)(x + 2)- 3(x^2 + 2x + 1)#
#color(blue)("Consider the "-3(x^2+2x+1))#
Multiply everything inside the brackets by (-3) giving:
#-3x^2-6x-3#
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#color(blue)("Consider the "5(x+3)(x+2))#
Multiply everything inside the first brackets by (+5):
#5(x+3) = 5x+15# giving:
#5(x+3)(x+2) ->color(red)((5x+15))color(green)( (x+2) )#
Multiply everything in the right bracket by everything in the left.
#color(green)( color(red)(5x)(x+2)color(white)("ddd")color(red)(+15)(x+2) )larr" Notice the + followed the 15"#
#5x^2ubrace(+10x color(white)("ddd")+15x)+30#
#5x^2 color(white)("dddd") +25xcolor(white)("dddd") +30#
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#color(blue)("Putting it all together")#
#5(x+3)(x+2) color(white)("ddd")- 3(x^2+2x+1) #
#5x^2+25x+30color(white)("ddd")-3x^2-6x-3#
Collecting like terms
#(5x^2-3x^2)+(25x-6x)+(30-3)#
#color(white)("ddd")2x^2color(white)("ddddddd")+19xcolor(white)("ddddd")+27#
#2x^2+19x+27#
