№1 Упростите выражение:

a) (y − 5)(y − 11) − 8(3 − 2) = y^2-16y+55-8 = y^2-16y+47

б) 5m(m − 4) − (10 −m )^2 = 5m^2-20-(100-20m+m^2)=4m^2+20m-120

в) 16t + 2(t − 4)^2 = 16t + 2(t^2-8t+16)=2t^2+32
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№2 Разложите на множители:

а) 36m − m^3 = m(36-m^2)=m(6-m)(6+m)

б) −7b^2 − 14bc − 7c^2 = -7(b^2+2bc+c^2)=-7(b+c)^2
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№3 Упростите выражение:

m^2 (4m + 3) + (2m −m ^2)^2 − m^2 (m + 2)( m− 2) =
= m^2 (4m + 3) + m^2(2 −m)^2 − m^2 (m + 2)( m− 2) =
= m^2 (4m + 3) + m^2(m-2)^2 − m^2 (m + 2)( m− 2) =
= m^2 (4m + 3) + m^2(m-2)(m-2-(m+2)) =m^2 (4m + 3)-4m^2(m-2) =
=m^2(4m+3-4(m-2))=m^2(4m+3-4m+8) = 11m^2

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№4 Разложите на множители:

a) f^4 - 81/16 = f^4 - (3/2)^4=(f^2-(3/2)^2)(f^2+(3/2)^2)=(f-3/2)(f+3/2)(f^2+9/4)

б) 625 − m^4 = 5^4-m^4=(5^2-m^2)(5^2+m^2)=(5-m)(5+m)(25+m^2)