y=(x+6)(x+5)^2(x+10)^2y=(x+6)(x+5)2(x+10)2
FOIL (x+5)^2(x+5)2:
y=(x+6)(x^2+10x+25)(x+10)^2y=(x+6)(x2+10x+25)(x+10)2
FOIL (x+10)^2(x+10)2:
y=(x+6)(x^2+10x+25)(x^2+20x+100)y=(x+6)(x2+10x+25)(x2+20x+100)
Distribute the first two sections within parentheses:
y=[(x+6)(x^2)+(x+6)(10x)+(x+6)(25)][x^2+20x+100]y=[(x+6)(x2)+(x+6)(10x)+(x+6)(25)][x2+20x+100]
Simplify:
y={[(x^2)(x)+(x^2)(6)]+[(10x)(x)+(10x)(6)]+[(25)(x)+(25)(6)]}[x^2+20x+100]y={[(x2)(x)+(x2)(6)]+[(10x)(x)+(10x)(6)]+[(25)(x)+(25)(6)]}[x2+20x+100]
Simplify further:
y=(x^3+6x^2+10x^2+60x+25x+150)(x^2+20x+100)y=(x3+6x2+10x2+60x+25x+150)(x2+20x+100)
Combine like terms within the first parentheses:
y=(x^3+16x^2+85x+150)(x^2+20x+100)y=(x3+16x2+85x+150)(x2+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)]y=[(x2+20x+100)(x3)]+[(x2+20x+100)(16x2)]+[(x2+20x+100)(85x)]+[(x2+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
