Question

Restrangeti, folosind patratul sumei a trei termeni:
a) 49- 2xy- 14x+ 14y+ x²+ y²
b) 36+ y²+ 4x²- 4xy+ 24x- 12y

Answer 1

(a+b+c)²=a²+b²+c²+2ab+2bc+2ac

a) 49- 2xy- 14x+ 14y+ x²+ y²=

=7²+x²+y²-14x+-2xy+14y

=7²+x²+y²+2•7•(-x)+2•(-x)•y +2•7•y

=(7-x+y)²

b) 36+ y²+ 4x²- 4xy+ 24x- 12y =

=6²+y²+4x²-12y-4xy+24x

=6²+y²+(2x)²+2•6•(-y)+2•(-y)•(2x)+2•6•(2x)

=(6-y+2x)²