II gimnazjum

Matematyka z plusem 2

a) (x+3)2=(x+3)(x+3)=x⋅x+x⋅3+3⋅x+3⋅3=x2+6x+9

P□​=a2

Pole trójkąta prostokątnego to połowa iloczynu jego przyprostokątnych.

pierwsza liczba: 10-x druga liczba: 20-(10-x)=20-10+x=10+x (10−x)2+(10+x)2=100−10x−10x+x2+100+10x+10x+x2=200+2x2

a) (x−1)(x3+x2+x+1)=x⋅x3+x⋅x2+x⋅x+x⋅1−x3−x2−x−1=x4+x3+x2+x−x3−x2−x−1=x4−1

a) (x+1)(x+2)(x+3)=(x2+2x+x+2)(x+3)=(x2+3x+2)(x+3)=x2⋅x+x2⋅3+3x⋅x+3x⋅3+2x+2⋅3=x3+6x2+11x+6

<img style="vertical-align: middle;" src="../../../math/formula?%5Cdisplaystyle%7Ba%7D%7B%5C)%7D%5C%20%7B%5Cleft(%7Bx%7D%2B%7B1%7D%5Cright)%7D%7B%5Cleft(%7Bx%7D-%7B2%7D%5Cright)%7D%2B%7B%5Cleft(%7Bx%7D%2B%7B2%7D%5Cright)%7D%7B%5Cleft(%7Bx%7D-%7B1%7D%5Cright)%7D%3D%7B%7Bx%7D%7D%5E%7B%7B2%7D%7D%2B%7Bx%7D-%7B2%7D%7Bx%7D-%7B2%7D%2B%7B%7Bx%7D%7D%5E%7B%7B2%7D%7D%2B%7B2%7D%7Bx%7D-%7Bx%7D-%7B2%7D%3D%7B2%7D%7B%7Bx%7D%7D%5E%7B%7B2%7D%7D-%7B4%7D"> b) (5k+n)(k−2n)−k(4k+n)=5k2+nk−10nk−2n2−4k2−nk=k2−10kn−2n2

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