8. ročníkVýrazyVýrazy Vzorce (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2 (a+b)2=a2+2ab+b2 (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2 (a−b)2=a2−2ab+b2 (a+b)(a−b)=a2−b2(a + b)(a - b) = a^2 - b^2 (a+b)(a−b)=a2−b2 1) Vypočtěte (x+2)2=(x + 2)^2 = (x+2)2=(3a+1)2=(3a + 1)^2 = (3a+1)2=(2m+5n)2=(2m + 5n)^2 = (2m+5n)2=(y−3)2=(y - 3)^2 = (y−3)2=(4b−1)2=(4b - 1)^2 = (4b−1)2=(3p−2q)2=(3p - 2q)^2 = (3p−2q)2=(z+4)(z−4)=(z + 4)(z - 4) = (z+4)(z−4)=(5c+2)(5c−2)=(5c + 2)(5c - 2) = (5c+2)(5c−2)=(x2+y)(x2−y)=(x^2 + y)(x^2 - y) = (x2+y)(x2−y)=ZkontrolovatZobrazit řešení 2) Vypočtěte (a+1)2−(a−1)2=(a + 1)^2 - (a - 1)^2 = (a+1)2−(a−1)2=(2x−3)2+(2x+3)(2x−3)=(2x - 3)^2 + (2x + 3)(2x - 3) = (2x−3)2+(2x+3)(2x−3)=(m+n)2−(m−n)(m+n)=(m + n)^2 - (m - n)(m + n) = (m+n)2−(m−n)(m+n)=(x2+3)2=(x^2 + 3)^2 = (x2+3)2=(y3−2)2=(y^3 - 2)^2 = (y3−2)2=(a+b2)(a−b2)=(a + b^2)(a - b^2) = (a+b2)(a−b2)=ZkontrolovatZobrazit řešení 3) Rozložte na součin x2+6x+9=x^2 + 6x + 9 = x2+6x+9=4a2−4a+1=4a^2 - 4a + 1 = 4a2−4a+1=9m2+12mn+4n2=9m^2 + 12mn + 4n^2 = 9m2+12mn+4n2=y2−25=y^2 - 25 = y2−25=16b2−1=16b^2 - 1 = 16b2−1=x4−9y2=x^4 - 9y^2 = x4−9y2=49p2−64q2=49p^2 - 64q^2 = 49p2−64q2=81−a2b2=81 - a^2b^2 = 81−a2b2=14m2−916n2=\frac{1}{4}m^2 - \frac{9}{16}n^2 = 41m2−169n2=ZkontrolovatZobrazit řešení 4) Zjednodušte x2−4x+2=\frac{x^2 - 4}{x + 2} = x+2x2−4=(a−1)2a2−1=\frac{(a - 1)^2}{a^2 - 1} = a2−1(a−1)2=m3+1m2−m+1=\frac{m^3 + 1}{m^2 - m + 1} = m2−m+1m3+1=y2−9y−3=\frac{y^2 - 9}{y - 3} = y−3y2−9=b2−4b+4b−2=\frac{b^2 - 4b + 4}{b - 2} = b−2b2−4b+4=p3−8p2+2p+4=\frac{p^3 - 8}{p^2 + 2p + 4} = p2+2p+4p3−8=ZkontrolovatZobrazit řešení 5) Vypočtěte (x+y+z)2=(x + y + z)^2 = (x+y+z)2=(a−b+c)2=(a - b + c)^2 = (a−b+c)2=(m+n+1)(m+n−1)=(m + n + 1)(m + n - 1) = (m+n+1)(m+n−1)=(p−q−r)2=(p - q - r)^2 = (p−q−r)2=((a−b)+c)2=((a - b) + c)^2 = ((a−b)+c)2=((x+2)+y)((x+2)−y)=((x + 2) + y)((x + 2) - y) = ((x+2)+y)((x+2)−y)=(x2+2x+1)−(x+1)2=(x^2 + 2x + 1) - (x + 1)^2 = (x2+2x+1)−(x+1)2=(x2+1)2−(x2−1)2=(x^2 + 1)^2 - (x^2 - 1)^2 = (x2+1)2−(x2−1)2=ZkontrolovatZobrazit řešení 6) Vypočtěte (x+3)2−(x2+9)=(x + 3)^2 - (x^2 + 9) = (x+3)2−(x2+9)=(2a−1)2+4a=(2a - 1)^2 + 4a = (2a−1)2+4a=(m+2)(m−2)−(m−1)2=(m + 2)(m - 2) - (m - 1)^2 = (m+2)(m−2)−(m−1)2=(y−5)2−(y2−25)=(y - 5)^2 - (y^2 - 25) = (y−5)2−(y2−25)=(3b+2)2−12b=(3b + 2)^2 - 12b = (3b+2)2−12b=(p−3)(p+3)−(p+1)2=(p - 3)(p + 3) - (p + 1)^2 = (p−3)(p+3)−(p+1)2=(a+b)2−(a−b)2=(a + b)^2 - (a - b)^2 = (a+b)2−(a−b)2=(2x−y)2−(2x+y)(2x−y)=(2x - y)^2 - (2x + y)(2x - y) = (2x−y)2−(2x+y)(2x−y)=(x2+y2)2−(x2−y2)2=(x^2 + y^2)^2 - (x^2 - y^2)^2 = (x2+y2)2−(x2−y2)2=(2a+b−c)2=(2a + b - c)^2 = (2a+b−c)2=(3m−n)−2)((3m−n)+2=(3m - n) - 2)((3m - n) + 2 = (3m−n)−2)((3m−n)+2=(x−y+z)2=(x - y + z)^2 = (x−y+z)2=ZkontrolovatZobrazit řešeníNaposledy aktualizováno 6. května 2025VálecCelistvé výrazy