Answer:
[tex]\mathrm{True\:for\:all}\:x[/tex]
Step-by-step explanation:
[tex]\left(2x+3y\right)^2-24xy=\left(2x-3y\right)^2[/tex]
[tex]\left(2x+3y\right)^2-24xy[/tex]
[tex]=4x^2+12xy+9y^2-24xy[/tex]
[tex]=9y^2-12xy+4x^2[/tex]
[tex]\left(2x-3y\right)^2[/tex]
[tex]a=2x,\:\:b=3y[/tex]
[tex]=\left(2x\right)^2-2\cdot \:2x\cdot \:3y+\left(3y\right)^2[/tex]
[tex]=4x^2-12xy+9y^2[/tex]
[tex]9y^2-12xy+4x^2=4x^2-12xy+9y^2[/tex]
[tex]\mathrm{Subtract\:}9y^2\mathrm{\:from\:both\:sides}[/tex]
[tex]9y^2-12xy+4x^2-9y^2=4x^2-12xy+9y^2-9y^2[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]-12xy+4x^2=4x^2-12xy[/tex]
[tex]\mathrm{Subtract\:}4x^2-12xy\mathrm{\:from\:both\:sides}[/tex]
[tex]-12xy+4x^2-\left(4x^2-12xy\right)=4x^2-12xy-\left(4x^2-12xy\right)[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]0=0[/tex]
[tex]\mathrm{Both\:sides\:are\:equal}[/tex]
[tex]\mathrm{True\:for\:all}\:x[/tex]
