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`@` `\text {Ans}`
`\downarrow`
`(2x - 3)^2 - (2x + 3)^2`
`= 4x^2 - 12x + 9 - (4x^2 + 12x + 9)`
`= 4x^2 - 12x + 9 - 4x^2 - 12x - 9`
`= (4x^2 - 4x^2) + (-12x - 12x) + (9-9)`
`= -24x`
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`@` CT:
`(A + B)^2 = A^2 + 2AB + B^2`
`(A - B)^2 = A^2 - 2AB + B^2`
\(\left(2x-3\right)^2-\left(2x+3\right)^2\)
\(=\left[\left(2x-3\right)+\left(2x+3\right)\right]\left[\left(2x-3\right)-\left(2x+3\right)\right]\)
\(=\left(2x-3+2x+3\right)\left(2x-3-2x-3\right)\)
\(=4x\cdot-6\)
\(=-24x\)
Ta có: \(\dfrac{1}{2+\sqrt{3}}+\sqrt{3}\)
\(=2-\sqrt{3}+\sqrt{3}\)
=2
Ta có: \(\dfrac{\sqrt{8-2\sqrt{12}}}{\sqrt{3}-1}\)
\(=\dfrac{\sqrt{\left(\sqrt{6}-\sqrt{2}\right)^2}}{\sqrt{3}-1}\)
\(=\sqrt{2}\)
Ta có: \(\dfrac{2\sqrt{3}}{\sqrt{3}+\sqrt{2}}+\sqrt{24}\)
\(=2\sqrt{3}\left(\sqrt{3}-\sqrt{2}\right)+2\sqrt{6}\)
\(=6-2\sqrt{6}+2\sqrt{6}\)
=6
(x-y)3+(x+y)3+(y-x)3-3xy(x+y)
=x3-3x2y+3xy2-y3+x3+3x2y+3xy2+y3+y3-3y2x+3yx2-x3-3x2y-3xy2
=x3+x3-x3-3x2y+3x2y-3yx2-3x2y+3xy2+3xy2-3y2x-3xy2-y3+y3+y3
=x3+y3
