Question

Thực hiện phép tính

a) x .(x+4) .(x-4) - ( x^2+1) (x^2-1)

b ) (y-3).(y+3) .(y^2+9) - (y^2 +2) .(y^2 -2 ) 

c) (a+b-c)^2 - (a-c)^2 -2ab + 2bc 
 

Answer 1

a) x-16x-1

b)y²-77

c) b²

Answer 2

b) \(=\left(y^2-9\right)\left(y^2+9\right)-\left(y^2+2\right)\left(y^2-2\right)\)

\(=y^4-81-y^4+4\)\(=-77\)

Answer 3

A.   \(x.\left(x+4\right).\left(x-4\right)-\left(x^2+1\right)\left(x^2-1\right)\)

\(=x.\left(x^2-4x+4x-16\right)-\left(x^4-1x^2+1x^2-1\right)\)

\(=x^3-4x^2+4x^2-16x-x^4+1x^2-1x^2-1\)

\(=-x^4+x^3-16x-1\)

B.   \(\left(y-3\right).\left(y+3\right).\left(y^2+9\right)-\left(y^2+2\right).\left(y^2-2\right)\)

\(=\left(y-3\right).\left(y^3+9y+3y^2+27\right)-\left(y^4-2y+2y^2-4\right)\)

\(=y^4+9y^2+3y^3+27y-3y^3-27y-9y^2-81-y^4+2y-2y^2+4\)

\(=-2y^2-77\)

C.  \(\left(a+b-c\right)^2-\left(a-c\right)^2-2ab+2bc\)

\(=a^2+b^2+c^2+2ab-2bc-2ac-a^2-2ac+c^2-2ab+2bc\)

\(=2c^2+b^2-4ac\)