How do you simplify #5(x + 3)(x + 2)- 3(x^2 + 2x + 1)#?

1 Answer
May 13, 2018

Answer:

#2x^2+19x+27#

Explanation:

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#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#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#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#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#