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Ytochka33d
@Ytochka33d
November 2021
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Godnessgirl
A) х³-4х²y+4xy²=x(x²-4xy+4y²)=x(x-2y)²
б) pt²+6p²t+9p³=p(t²+6pt+9p²)=p(t+3p)²
в) 4а³+12а²b+9ab²=a(4a²+12ab+9b²)=a(2a+3b)²
г) 9х³у-12х²у²+4ху³=ху(9х²-12ху+4у²)=
=ху(3х-2у)²
д) х²(х-1)+4х(х-1)+4(х-1)=(х-1)(х²+4х+4)=(х-1)(х+2)²
е) 36(у+2)+12у(у+2)=12(у+2)(3+у)
ж) 25х²(х²-1)-10х(х²-1)+х²-1=(х²-1)(25х²-10х+1)=
=(х-1)(х+1)(5х-1)²
з) 9а²(а²-b²)+12ab(a²-b²)+4b²(a²-b²)=
=(a²-b²)(9a²+12ab+4b²)=(a-b)(a+b)(3a+2b)²
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Answers & Comments
б) pt²+6p²t+9p³=p(t²+6pt+9p²)=p(t+3p)²
в) 4а³+12а²b+9ab²=a(4a²+12ab+9b²)=a(2a+3b)²
г) 9х³у-12х²у²+4ху³=ху(9х²-12ху+4у²)=
=ху(3х-2у)²
д) х²(х-1)+4х(х-1)+4(х-1)=(х-1)(х²+4х+4)=(х-1)(х+2)²
е) 36(у+2)+12у(у+2)=12(у+2)(3+у)
ж) 25х²(х²-1)-10х(х²-1)+х²-1=(х²-1)(25х²-10х+1)=
=(х-1)(х+1)(5х-1)²
з) 9а²(а²-b²)+12ab(a²-b²)+4b²(a²-b²)=
=(a²-b²)(9a²+12ab+4b²)=(a-b)(a+b)(3a+2b)²