Question

Rút gọn biểu thức :

a .5 . ( x + 2 ) . ( x - 2 ) - ( 3 - 4x )²

b . 2 . ( x - y ) . ( x + y ) + ( x + y )² + ( x - y )²

c . ( x - y + z )² + ( x - y )² + 2 ( x - y + z ) . ( y - z )

Answer 1

Lời giải:

Áp dụng các HĐT đáng nhớ:

a)

\(5(x+2)(x-2)-(3-4x)^2=5(x^2-2^2)-(9-24x+16x^2)\)

\(=5x^2-20-9+24x-16x^2\)

\(=-11x^2+24x-29\)

b)

\(2(x-y)(x+y)+(x+y)^2+(x-y)^2\)

\(=2(x^2-y^2)+(x^2+2xy+y^2)+(x^2-2xy+y^2)\)

\(=2x^2-2y^2+2x^2+2y^2=4x^2\)

c)

\((x-y+z)^2+(x-y)^2+2(x-y+z)(y-z)\)

\(=(x-y+z)^2+2(x-y+z)(y-z)+(y-z)^2+(x-y)^2-(y-z)^2\)

\(=(x-y+z+y-z)^2+(x-y)^2-(y-z)^2\)

\(=x^2+(x-y)^2-(y-z)^2=x^2+x^2-2xy+y^2-(y^2-2yz+z^2)\)

\(=2x^2-2xy+2yz-z^2\)