a) \(x\left(x-3\right)\left(x+3\right)-\left(x^2-2\right)\left(x^2+2\right)\)
\(=x\left(x^2-9\right)-x^4+4\)
\(=x^3-9x-x^4+4\)
\(=-x^4+x^3-9x+4\)
b) \(\left(y+2\right)\left(y-2\right)\left(y^2+4\right)-\left(y^2-3\right)\left(y^2+3\right)\)
\(=\left(y^2-4\right)\left(y^2+4\right)-y^4+9\)
\(=y^4-16-y^4+9\)
\(=-7\)
c) \(\left(a-b+c\right)^2+\left(b-c\right)^2+2\left(a-b+c\right)\left(c-b\right)\)
\(=\left(a-b+c\right)^2-2\left(a-b+c\right)\left(b-c\right)+\left(b-c\right)^2\)
\(=\left[\left(a-b+c\right)-\left(b+c\right)\right]^2\)
\(=\left(a-2b\right)^2\)
\(=a^2-4ab+4b^2\)
a) x( x - 3 )( x + 3 ) - ( x2 - 2 )( x2 + 2 )
= x( x2 - 9 ) - ( x4 - 4 )
= x3 - 3x - x4 + 4
= -x4 + x3 - 3x + 4
b) ( y + 2 )( y - 2 )( y2 + 4 ) - ( y2 - 3 )( y2 + 3 )
= ( y2 - 4 )( y2 + 4 ) - ( y4 - 9 )
= y4 - 16 - y4 + 9
= -7
c) ( a - b + c )2 + ( b - c )2 + 2( a - b + c )( c - b )
= ( a - b + c )2 - 2( a - b + c )( b - c ) + ( b - c )2
= [ ( a - b + c ) - ( b - c ) ]2
= ( a - b + c - b + c )2
= ( a - 2b + 2c )2
= [ ( a - 2b ) + 2c ]2
= ( a - 2b )2 + 2( a - 2b )2c + ( 2c )2
= a2 - 4ab + 4b2 + 4ac - 8bc + 4c2
= a2 + 4b2 + 4c2 - 4ab - 8bc + 4ca
