II gimnazjum

Matematyka wokół nas 2

a)(n+2)⋅(n+3)=n2+3n+2n+6=n2+5n+6 b)(x−4)⋅(x+4)=x2+4x−4x−16=x2−16

a)(3−8x)⋅(3+8x)=9+24x−24x−64x2=9−64x2 b)(a−6)⋅(3a+4)=3a2+4a−18a−24=3a2−14a−24

a)(x+y+3)⋅(2x−y)=2x2−xy+2xy−y2+6x−3y=2x2+xy−y2+6x−3y b)(3x−1)⋅(3x+1)⋅(2−x)=(9x2+3x−3x−1)⋅(2−x)=(9x2−1)⋅(2−x)=18x2−9x3−2+x

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a)(x+y)⋅(x2−xy+y2)−(x3−y3)=(x3−x2y+xy2+x2y−xy2+y3)⋅(x3−y3)=(x3+y3)−(x3−y3)=x3+y3−x3+y3=2y3

a)&nbsp; I (trapez prostokątny) dłuższa podstawa: 2x−1+(x+1)=3x PI​=(2x−1+3x)⋅(x+2)⋅21​=(5x−1)⋅(x+2)⋅21​=21​⋅(5x2+10x−x−2)=21​⋅(5x2+9x−2) &nbsp; II (trapez prostokątny) dłuższa podstawa: 2x−1+x+1=3x

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