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A = (x - 2)2 + (x + 3)2 - 2.(x + 1)(x - 1)
A = (x - 2)2 + (x + 3)2 - 2.(x2 - 1)
A = x2 - 2.2x + 22 + x2 + 2.3x + 32 - 2x2 + 2
A = 2x + 15
\(A=\left(x-2\right)^2+\left(x+3\right)^2-2\left(x+1\right)\left(x-1\right)\)
\(A=x^2-4x+4+x^2+6x+9-2\left(x^2-1\right)\)
\(A=2x^2+2x+13-2x^2+2\)
\(A=2x+15\)
a) \(M=\left(2x\right)^2.\left(x^3-x\right)-2x^2.\left(x^3-x+1\right)-\left(2x-5x^2\right).x\)
\(=4x^2.\left(x^3-x\right)-2x^5+2x^3-2x^2-2x^2+5x^3\)
\(=4x^5-4x^3-2x^5+2x^3-2x^2-2x^2+5x^3\)
\(=\left(4x^5-2x^5\right)-\left(4x^3-2x^3-5x^3\right)-\left(2x^2+2x^2\right)\)
\(=2x^5+3x^3-4x^2\)
M = ( 2x )2( x3 - x ) - 2x2( x3 - x + 1 ) - ( 2x - 5x2 )x
= 4x2( x3 - x ) - 2x5 + 2x3 - 2x2 - 2x2 + 5x3
= 4x5 - 4x3 - 2x5 + 2x3 - 2x2 - 2x2 + 5x3
= 2x5 + 3x3 - 4x2
a) \(x\left(xy+1\right)+y\left(xy-1\right)-xy\left(x+y\right)\)
\(=X^2y+x+xy^2-y-x^2y-xy^2\)
\(=x-y\)
(x2 - 1) / (x + 1)
=(x-1)(x+1)/x+1
=x-1
\(\frac{x^2-1}{x+1}=\frac{x^2+x-x-1}{x+1}=\frac{x.\left(x+1\right)}{x+1}-\frac{x+1-2}{x+1}=x-\frac{x+1}{x+1}+\frac{2}{x+1}=x-1+\frac{2}{x+1}\)