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