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\frac{1}{4}x^{2}-x+1+\left(\frac{1}{2}x-1\right)\left(\frac{1}{2}x+1\right)+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}x-1\right)\left(-\frac{1}{2}x+1\right)
Uporabite binomski izrek \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, da razširite \left(\frac{1}{2}x-1\right)^{2}.
\frac{1}{4}x^{2}-x+1+\left(\frac{1}{2}x\right)^{2}-1+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}x-1\right)\left(-\frac{1}{2}x+1\right)
Razmislite o \left(\frac{1}{2}x-1\right)\left(\frac{1}{2}x+1\right). Množenje je lahko preoblikovano v razliko kvadratov s pravilom: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Kvadrat števila 1.
\frac{1}{4}x^{2}-x+1+\left(\frac{1}{2}\right)^{2}x^{2}-1+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}x-1\right)\left(-\frac{1}{2}x+1\right)
Razčlenite \left(\frac{1}{2}x\right)^{2}.
\frac{1}{4}x^{2}-x+1+\frac{1}{4}x^{2}-1+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}x-1\right)\left(-\frac{1}{2}x+1\right)
Izračunajte potenco \frac{1}{2} števila 2, da dobite \frac{1}{4}.
\frac{1}{2}x^{2}-x+1-1+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}x-1\right)\left(-\frac{1}{2}x+1\right)
Združite \frac{1}{4}x^{2} in \frac{1}{4}x^{2}, da dobite \frac{1}{2}x^{2}.
\frac{1}{2}x^{2}-x+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}x-1\right)\left(-\frac{1}{2}x+1\right)
Odštejte 1 od 1, da dobite 0.
\frac{1}{2}x^{2}-x+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}x\right)^{2}-1
Razmislite o \left(-\frac{1}{2}x-1\right)\left(-\frac{1}{2}x+1\right). Množenje je lahko preoblikovano v razliko kvadratov s pravilom: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Kvadrat števila 1.
\frac{1}{2}x^{2}-x+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}\right)^{2}x^{2}-1
Razčlenite \left(-\frac{1}{2}x\right)^{2}.
\frac{1}{2}x^{2}-x+\left(\frac{1}{2}x+1\right)^{2}+\frac{1}{4}x^{2}-1
Izračunajte potenco -\frac{1}{2} števila 2, da dobite \frac{1}{4}.
\frac{3}{4}x^{2}-x+\left(\frac{1}{2}x+1\right)^{2}-1
Združite \frac{1}{2}x^{2} in \frac{1}{4}x^{2}, da dobite \frac{3}{4}x^{2}.
\frac{3}{4}x^{2}-x+\frac{1}{4}x^{2}+x+1-1
Uporabite binomski izrek \left(a+b\right)^{2}=a^{2}+2ab+b^{2}, da razširite \left(\frac{1}{2}x+1\right)^{2}.
x^{2}-x+x+1-1
Združite \frac{3}{4}x^{2} in \frac{1}{4}x^{2}, da dobite x^{2}.
x^{2}+1-1
Združite -x in x, da dobite 0.
x^{2}
Odštejte 1 od 1, da dobite 0.
\frac{1}{4}x^{2}-x+1+\left(\frac{1}{2}x-1\right)\left(\frac{1}{2}x+1\right)+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}x-1\right)\left(-\frac{1}{2}x+1\right)
Uporabite binomski izrek \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, da razširite \left(\frac{1}{2}x-1\right)^{2}.
\frac{1}{4}x^{2}-x+1+\left(\frac{1}{2}x\right)^{2}-1+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}x-1\right)\left(-\frac{1}{2}x+1\right)
Razmislite o \left(\frac{1}{2}x-1\right)\left(\frac{1}{2}x+1\right). Množenje je lahko preoblikovano v razliko kvadratov s pravilom: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Kvadrat števila 1.
\frac{1}{4}x^{2}-x+1+\left(\frac{1}{2}\right)^{2}x^{2}-1+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}x-1\right)\left(-\frac{1}{2}x+1\right)
Razčlenite \left(\frac{1}{2}x\right)^{2}.
\frac{1}{4}x^{2}-x+1+\frac{1}{4}x^{2}-1+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}x-1\right)\left(-\frac{1}{2}x+1\right)
Izračunajte potenco \frac{1}{2} števila 2, da dobite \frac{1}{4}.
\frac{1}{2}x^{2}-x+1-1+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}x-1\right)\left(-\frac{1}{2}x+1\right)
Združite \frac{1}{4}x^{2} in \frac{1}{4}x^{2}, da dobite \frac{1}{2}x^{2}.
\frac{1}{2}x^{2}-x+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}x-1\right)\left(-\frac{1}{2}x+1\right)
Odštejte 1 od 1, da dobite 0.
\frac{1}{2}x^{2}-x+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}x\right)^{2}-1
Razmislite o \left(-\frac{1}{2}x-1\right)\left(-\frac{1}{2}x+1\right). Množenje je lahko preoblikovano v razliko kvadratov s pravilom: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Kvadrat števila 1.
\frac{1}{2}x^{2}-x+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}\right)^{2}x^{2}-1
Razčlenite \left(-\frac{1}{2}x\right)^{2}.
\frac{1}{2}x^{2}-x+\left(\frac{1}{2}x+1\right)^{2}+\frac{1}{4}x^{2}-1
Izračunajte potenco -\frac{1}{2} števila 2, da dobite \frac{1}{4}.
\frac{3}{4}x^{2}-x+\left(\frac{1}{2}x+1\right)^{2}-1
Združite \frac{1}{2}x^{2} in \frac{1}{4}x^{2}, da dobite \frac{3}{4}x^{2}.
\frac{3}{4}x^{2}-x+\frac{1}{4}x^{2}+x+1-1
Uporabite binomski izrek \left(a+b\right)^{2}=a^{2}+2ab+b^{2}, da razširite \left(\frac{1}{2}x+1\right)^{2}.
x^{2}-x+x+1-1
Združite \frac{3}{4}x^{2} in \frac{1}{4}x^{2}, da dobite x^{2}.
x^{2}+1-1
Združite -x in x, da dobite 0.
x^{2}
Odštejte 1 od 1, da dobite 0.
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