Question

1. Розклади многочлен на множники способом групування.
a) am – bm + an – bn – ap + bp;
б) mt³ + nt³ + mt² - pt³ + nt²– pt²;
в) 4х³ + 12xyz + 28xy² – 3x²z– 9yz² - 21zу²
г) 10m² - 5m²n + 2n² – 4m + 2mn - 5mn²​

Answer 1

$a) am-bm+an-bn-ap+bp=a\cdot(m+n-p)-b\cdot(m+n-p)=(m+n-p)\cdot(a-b)\\b)mt^3+nt^3+mt^2-pt^3+nt^2-pt^2=t^2\cdot(mt+nt+m-pt+n-p)=t^2\cdot(t\cdot(m+n-p)+m+n-p)=t^2\cdot(m+n-p)\cdot(t+1)\\c)4x^3+12xyz+28xy^2-3x^2z-9yz^2-21zy^2=4x\cdot(x^2+3yz+7y^2)-3z\cdot(x^2+3yz+7y^2)=(x^2+3yz+7y^2)\cdot(4x-3z)\\d)10m^2-5m^2n+2n^2-4m+2mn-5mn^2=5m\cdot(2m-mn-n^2)+2(n^2-2m+mn)=5m\cdot(2m-mn-n^2)+2\cdot(-(2m-mn-n^2))=5m\cdot(2m-mn-n^2)-2(2m-mn-n^2)=(2m-mn-n^2)\cdot(5m-2)$