I gimnazjum

Policzmy to razem 1

a) (x+1)(x+2)=x(x+2)+1(x+2)= &nbsp; x2+2x+x+2= &nbsp; x2+3x+2 &nbsp; &nbsp; b) (2a+3)(a+4)=

a) (3x+y)(2y+x)= &nbsp; 3x(2y+x)+y(2y+x)= &nbsp;    =6xy+3x2+2y2+yx= &nbsp; 3x2+2y2+7xy &nbsp; &nbsp; b) (4+xy)(x+y)= &nbsp; 4(x+y)+xy(x+y)= &nbsp;&nbsp;    =4x+4y+x2y+xy2

PI​=(2x+y)(x−2y)= &nbsp; 2x(x−2y)+y(x−2y)= &nbsp;     =2x2−4xy+xy−2y2= &nbsp; 2x2−3xy−2y2 &nbsp; &nbsp; PII​=(2x+y)(y+3x)= &nbsp; 2x(y+3x)+y(y+3x)= &nbsp;      =2xy+6x2+y2+3xy=

a) (32​x+4)(121​x2+6x+3)= &nbsp; (32​x+4)(23​x2+6x+3)= &nbsp;    =32​x(23​x2+6x+3)+4(23​x2+6x+3)= &nbsp;    =x3+312​x2+2x+212​x2+24x+12=

a) (m+2)(m2+4m+1)= &nbsp; m(m2+4m+1)+2(m2+4m+1)= &nbsp;&nbsp;    =m3+4m2+m+2m2+8m+2= &nbsp; m3+6m2+9m+2 &nbsp; &nbsp; b) (x+3)(3x2+4x+2)= &nbsp; x(3x2+4x+2)+3(3x2+4x+2)=

Wzory skróconego mnożenia:&nbsp; (□+Δ)2= &nbsp; □2+2⋅□⋅Δ+Δ2 &nbsp; (□−Δ)2=□2−2⋅□⋅Δ+Δ2 &nbsp; (□−Δ)⋅(□+Δ)=□2−Δ2

a) (3x+12)⋅62x−4​= &nbsp; (3x+12)⋅3x−2​= &nbsp; (31x+124)⋅(x−2)⋅311​= &nbsp;    =(x+4)(x−2)=x(x−2)+4(x−2)= &nbsp; x2−2x+4x−8= &nbsp; x2+2x−8 &nbsp; &nbsp; b) 57−2x​⋅(−7−2x)=

a) (5x2y3+xy4)(2x3y2+3xy)= &nbsp; 5x2y3(2x3y2+3xy)+xy4(2x3y2+3xy)= &nbsp;    =10x5y5+15x3y4+2x4y6+3x2y5

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