a, \(\left(x+y\right)^2+\left(x-y\right)^2-2\left(x-y\right)\left(x+y\right)\)
\(=x^2+2xy+y^2+x^2-2xy+y^2-2\left(x^2+xy-xy-y^2\right)\)
\(=2x^2+2y^2-2x^2+2y^2\)
\(=4y^2\)
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d, (x2+4)(x+2)(x-2) -(x2-3)2
=(x2+4)(x2 - 4) -(x2-3)2
= (x2)2-42 - [(x2)2 -6x2 +9]
=x4 -16 -x4+6x2 -9
= 6x2 -25
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a, ( x+y)2 +(x-y)2 - 2(x-y)(x+y)
= x2 +2xy +y2 + x2-2xy+y2- 2(x2-y2)
= 2x2 + 2y2 -2x2+2y2
=4y2
b, (11x +9y)2-(11x+9y)(11x-9y) -162y2
= 121x2 + 198xy +81y2 -(121x2 -81y2) -162y2
= (121x2-121x2) + 198xy + (81y2 +81y2-162y2)
= 198xy
c, 5(3-2x)2 - 3(3x+1)(3x-1) +7x2-48
= 5(32 - 12x +4x2) - 3(9x2-1) +7x2-48
= 45 -60x +20x2 -27x2 +3 +7x2-48
= (45+3-48) +(20x2+7x2-27x2) -60x
=-60x