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11 votes
Simplify the expression to a polynomial in standard form:

(
3
x
+
5
)
(
2
x
2
+
x
+
5
)
(3x+5)(2x
2
+x+5)

User Casieber
by
5.2k points

1 Answer

7 votes

Answer:

9x

4

+120x

3

+550x

2

+1000x+100x2

2

+500x2+625+18x

3

x2+150x

2

x2+350×2+50x2x+60×2

2

+30x

2

x2+150×2+36x

2

x2

2

+18x

3

x2+90x

2

x2+60×2

2

+30x

2

x2+150×2

Explanation:

(3x+5)(2x2+x+5)(3x+5)(2x2+x+5)

=(6×2+3x

2

+15x+10x2+5x+25)(3x+5)(2x2+x+5)=

=(3x

2

+20x+10x2+25+6×2)(3x+5)(2x2+x+5)=

=(9x

3

+15x

2

+60x

2

+100x+30×2+50x2+75x+125+6×2⋅3x+6×2⋅5)(2x2+x+5)=

=(9x

3

+15x

2

+60x

2

+100x+30×2+50x2+75x+125+18x

2

x2+6×2⋅5)(2x2+x+5)=

=(9x

3

+15x

2

+60x

2

+100x+30×2+50x2+75x+125+18x

2

x2+30×2)(2x2+x+5)=

=(9x

3

+75x

2

+175x+50x2+125+30×2+18x

2

x2+30×2)(2x2+x+5)=

=18x

3

x2+9x

4

+45x

3

+150x

2

x2+75x

3

+375x

2

+350×2+175x

2

+875x+100x2

2

+50x2x+250x2+250x2+125x+625+30×2⋅2x2+30×2x+30×2⋅5+18x

2

x2⋅2x2+18x

2

x2x+18x

2

x2⋅5+30×2⋅2x2+30×2x+30×2⋅5=

=18x

3

x2+9x

4

+45x

3

+150x

2

x2+75x

3

+375x

2

+350×2+175x

2

+875x+100x2

2

+50x2x+250x2+250x2+125x+625+60×2

2

+30×2x+30×2⋅5+18x

2

x2⋅2x2+18x

2

x2x+18x

2

x2⋅5+30×2⋅2x2+30×2x+30×2⋅5=

=18x

3

x2+9x

4

+45x

3

+150x

2

x2+75x

3

+375x

2

+350×2+175x

2

+875x+100x2

2

+50x2x+250x2+250x2+125x+625+60×2

2

+30x

2

x2+30×2⋅5+18x

2

x2⋅2x2+18x

2

x2x+18x

2

x2⋅5+30×2⋅2x2+30×2x+30×2⋅5=

=18x

3

x2+9x

4

+45x

3

+150x

2

x2+75x

3

+375x

2

+350×2+175x

2

+875x+100x2

2

+50x2x+250x2+250x2+125x+625+60×2

2

+30x

2

x2+150×2+18x

2

x2⋅2x2+18x

2

x2x+18x

2

x2⋅5+30×2⋅2x2+30×2x+30×2⋅5=

=18x

3

x2+9x

4

+45x

3

+150x

2

x2+75x

3

+375x

2

+350×2+175x

2

+875x+100x2

2

+50x2x+250x2+250x2+125x+625+60×2

2

+30x

2

x2+150×2+36x

2

x2

2

+18x

2

x2x+18x

2

x2⋅5+30×2⋅2x2+30×2x+30×2⋅5=

=18x

3

x2+9x

4

+45x

3

+150x

2

x2+75x

3

+375x

2

+350×2+175x

2

+875x+100x2

2

+50x2x+250x2+250x2+125x+625+60×2

2

+30x

2

x2+150×2+36x

2

x2

2

+18x

3

x2+18x

2

x2⋅5+30×2⋅2x2+30×2x+30×2⋅5=

=18x

3

x2+9x

4

+45x

3

+150x

2

x2+75x

3

+375x

2

+350×2+175x

2

+875x+100x2

2

+50x2x+250x2+250x2+125x+625+60×2

2

+30x

2

x2+150×2+36x

2

x2

2

+18x

3

x2+90x

2

x2+30×2⋅2x2+30×2x+30×2⋅5=

=18x

3

x2+9x

4

+45x

3

+150x

2

x2+75x

3

+375x

2

+350×2+175x

2

+875x+100x2

2

+50x2x+250x2+250x2+125x+625+60×2

2

+30x

2

x2+150×2+36x

2

x2

2

+18x

3

x2+90x

2

x2+60×2

2

+30×2x+30×2⋅5=

=18x

3

x2+9x

4

+45x

3

+150x

2

x2+75x

3

+375x

2

+350×2+175x

2

+875x+100x2

2

+50x2x+250x2+250x2+125x+625+60×2

2

+30x

2

x2+150×2+36x

2

x2

2

+18x

3

x2+90x

2

x2+60×2

2

+30x

2

x2+30×2⋅5=

=18x

3

x2+9x

4

+45x

3

+150x

2

x2+75x

3

+375x

2

+350×2+175x

2

+875x+100x2

2

+50x2x+250x2+250x2+125x+625+60×2

2

+30x

2

x2+150×2+36x

2

x2

2

+18x

3

x2+90x

2

x2+60×2

2

+30x

2

x2+150×2=

=9x

4

+120x

3

+550x

2

+1000x+100x2

2

+500x2+625+18x

3

x2+150x

2

x2+350×2+50x2x+60×2

2

+30x

2

x2+150×2+36x

2

x2

2

+18x

3

x2+90x

2

x2+60×2

2

+30x

2

x2+150×2

User StNickolay
by
5.2k points