How do you multiply #(-13u+v^2)^2#?

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Answer 1 · 2018-03-08T14:13:33

#v^4-26uv^2+169u^2#

#(v^2-13u)^2#
#(v^2)^2-2(v^2)(13u)+(13u)^2#
#v^4-26uv^2+169u^2#

Answer 2 · 2018-03-08T14:15:57

The formula for #(a+b)^2# is #a^2+2ab+b^2#. Let's apply this to our problem.

#(-13u+v^2)^2# = #(-13u)^2+2(-13u)(v^2)+(v^2)^2#

#-13u*-13u = 169u^2#
#2(-13u)(v^2) = -26uv^2#
#v^2*v^2 = v^4#

Therefore, our answer is #169u^2-26uv^2+v^4#.

Answer 3 · 2018-03-08T14:16:54

#169u^2-26uv^2+v^4#

In general
#color(white)("XXX")(color(red)a+color(blue)b)^2=color(red)a^2+2color(red)acolor(blue)b+color(blue)b^2#

So
#color(white)("XXX")(color(red)(-13u)+color(blue)v^2))^2#

#color(white)("XXXXXXXX")=(color(red)(-13u))^2+2 * (color(red)(-13u)) * color(blue)(v^2) + (color(blue)(v^2))^2#

#color(white)("XXXXXXXX")=169u^2-26uv^2+v^4#