Given:#" "(x-2)^(color(red)(4)#
Use the line marked #color(red)(x^4)#
Notice there are a count of 5 numbers. This is the number of terms needed
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("How Pascal's Triangle is used in this context")#
#color(brown)("Suppose we had "(x+y)^4#
#color(brown)("Without using the numbers in the triangle our 5 terms would be:")#
#color(brown)(x^4y^0 + x^3y^1+x^2y^2+x^1y^3+x^0y^4)#
#color(green)("Now we put in the numbers from the triangle:")#
#color(brown)((color(green)(1)xxx^4y^0) +(color(green)(4)xx x^3y^1)+(color(green)(6)xxx^2y^2)+(color(green)(4)xxx^1y^3)(color(green)(1)xxx^0y^4))#
Remember that #x^0=1" ; "y^0=1#
#(x^4) +(4 x^3y)+(6x^2y^2)+(4xy^3)+(y^4)#
But from the question #color(blue)(y=-2)# giving:
#color(brown)((x^4) +(4 x^3xxcolor(blue)((-2)))+(6x^2xxcolor(blue)((-2))^2)+(4x xxcolor(blue)((-2))^3)+color(blue)((-2))^4)#
#(x^4) +(-8 x^3)+(24x^2)+(-32x)+16#
#x^4-8x^3+24x^2-32x+16#
