#y=(x+6)(x+5)^2(x+10)^2#
FOIL #(x+5)^2#:
#y=(x+6)(x^2+10x+25)(x+10)^2#
FOIL #(x+10)^2#:
#y=(x+6)(x^2+10x+25)(x^2+20x+100)#
Distribute the first two sections within parentheses:
#y=[(x+6)(x^2)+(x+6)(10x)+(x+6)(25)][x^2+20x+100]#
Simplify:
#y={[(x^2)(x)+(x^2)(6)]+[(10x)(x)+(10x)(6)]+[(25)(x)+(25)(6)]}[x^2+20x+100]#
Simplify further:
#y=(x^3+6x^2+10x^2+60x+25x+150)(x^2+20x+100)#
Combine like terms within the first parentheses:
#y=(x^3+16x^2+85x+150)(x^2+20x+100)#
Distribute:
#y=[(x^2+20x+100)(x^3)]+[(x^2+20x+100)(16x^2)]+[(x^2+20x+100)(85x)]+[(x^2+20x+100)(150)]#
Distribute further:
#y={[(x^3)(x^2)]+[(x^3)(20x)]+[(x^3)(100)]}+{[(16x^2)(x^2)]]+[(16x^2)(20x)]+[(16x^2)(100)]}+{[(85x)(x^2)]+[(85x)(20x)]+[(85x)(100)]}+{[(150)(x^2)]+[(150)(20x)]+[(150)(100)]}#
Simplify within brackets:
#y=x^5+20x^4+100x^3+16x^4+320x^3+1600x^2+85x^3+1700x^2+8500x+150x^2+3000x+15000#
Combine like terms:
#y=x^5+36x^4+505x^3+3450x^2+11500x+15000#
