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x^{2}
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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)
Brug binomialsætningen \left(a-b\right)^{2}=a^{2}-2ab+b^{2} til at udvide \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)
Overvej \left(\frac{1}{2}x-1\right)\left(\frac{1}{2}x+1\right). Multiplikation kan omdannes til differensen mellem kvadrater ved hjælp af reglen: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Kvadrér 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)
Udvid \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)
Beregn \frac{1}{2} til potensen af 2, og få \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)
Kombiner \frac{1}{4}x^{2} og \frac{1}{4}x^{2} for at få \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)
Subtraher 1 fra 1 for at få 0.
\frac{1}{2}x^{2}-x+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}x\right)^{2}-1
Overvej \left(-\frac{1}{2}x-1\right)\left(-\frac{1}{2}x+1\right). Multiplikation kan omdannes til differensen mellem kvadrater ved hjælp af reglen: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Kvadrér 1.
\frac{1}{2}x^{2}-x+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}\right)^{2}x^{2}-1
Udvid \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
Beregn -\frac{1}{2} til potensen af 2, og få \frac{1}{4}.
\frac{3}{4}x^{2}-x+\left(\frac{1}{2}x+1\right)^{2}-1
Kombiner \frac{1}{2}x^{2} og \frac{1}{4}x^{2} for at få \frac{3}{4}x^{2}.
\frac{3}{4}x^{2}-x+\frac{1}{4}x^{2}+x+1-1
Brug binomialsætningen \left(a+b\right)^{2}=a^{2}+2ab+b^{2} til at udvide \left(\frac{1}{2}x+1\right)^{2}.
x^{2}-x+x+1-1
Kombiner \frac{3}{4}x^{2} og \frac{1}{4}x^{2} for at få x^{2}.
x^{2}+1-1
Kombiner -x og x for at få 0.
x^{2}
Subtraher 1 fra 1 for at få 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)
Brug binomialsætningen \left(a-b\right)^{2}=a^{2}-2ab+b^{2} til at udvide \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)
Overvej \left(\frac{1}{2}x-1\right)\left(\frac{1}{2}x+1\right). Multiplikation kan omdannes til differensen mellem kvadrater ved hjælp af reglen: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Kvadrér 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)
Udvid \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)
Beregn \frac{1}{2} til potensen af 2, og få \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)
Kombiner \frac{1}{4}x^{2} og \frac{1}{4}x^{2} for at få \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)
Subtraher 1 fra 1 for at få 0.
\frac{1}{2}x^{2}-x+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}x\right)^{2}-1
Overvej \left(-\frac{1}{2}x-1\right)\left(-\frac{1}{2}x+1\right). Multiplikation kan omdannes til differensen mellem kvadrater ved hjælp af reglen: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Kvadrér 1.
\frac{1}{2}x^{2}-x+\left(\frac{1}{2}x+1\right)^{2}+\left(-\frac{1}{2}\right)^{2}x^{2}-1
Udvid \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
Beregn -\frac{1}{2} til potensen af 2, og få \frac{1}{4}.
\frac{3}{4}x^{2}-x+\left(\frac{1}{2}x+1\right)^{2}-1
Kombiner \frac{1}{2}x^{2} og \frac{1}{4}x^{2} for at få \frac{3}{4}x^{2}.
\frac{3}{4}x^{2}-x+\frac{1}{4}x^{2}+x+1-1
Brug binomialsætningen \left(a+b\right)^{2}=a^{2}+2ab+b^{2} til at udvide \left(\frac{1}{2}x+1\right)^{2}.
x^{2}-x+x+1-1
Kombiner \frac{3}{4}x^{2} og \frac{1}{4}x^{2} for at få x^{2}.
x^{2}+1-1
Kombiner -x og x for at få 0.
x^{2}
Subtraher 1 fra 1 for at få 0.
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