Question

2x+3y)^2– 24xy = (2x-3y)^2

Answer 1

`\mathrm{True\:for\:all}\:x`

Explanation:

`\left(2x+3y\right)^2-24xy=\left(2x-3y\right)^2`

`\left(2x+3y\right)^2-24xy`

`=4x^2+12xy+9y^2-24xy`

`=9y^2-12xy+4x^2`

`\left(2x-3y\right)^2`

`a=2x,\:\:b=3y`

`=\left(2x\right)^2-2\cdot \:2x\cdot \:3y+\left(3y\right)^2`

`=4x^2-12xy+9y^2`

`9y^2-12xy+4x^2=4x^2-12xy+9y^2`

`\mathrm{Subtract\:}9y^2\mathrm{\:from\:both\:sides}`

`9y^2-12xy+4x^2-9y^2=4x^2-12xy+9y^2-9y^2`

`\mathrm{Simplify}`

`-12xy+4x^2=4x^2-12xy`

`\mathrm{Subtract\:}4x^2-12xy\mathrm{\:from\:both\:sides}`

`-12xy+4x^2-\left(4x^2-12xy\right)=4x^2-12xy-\left(4x^2-12xy\right)`

`\mathrm{Simplify}`

`0=0`

`\mathrm{Both\:sides\:are\:equal}`

`\mathrm{True\:for\:all}\:x`