1)
а) 4x² +8x=4x(x+2).
б) 3m -6n +mn- 2n² =3(m-2n)+n(m-2n) =(m-2n)(n+3).
в) 9a² -16 =(3a)² -(4)² =(3a-4)(3a+4).
г) y³ +18y²+81y =y(y² +2y*9 +9²) =y(y+9)².
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2)
а) (36-a²)/(18+3a) =(6-a)(6+a)/3(6+a) =(6-a)/3.
б) (9p²-q²)/(9p² +6pq+q²)=(3p-q)(3p+q)/(3p+q)² =(3p-q)/(3p+q).
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3)
x³ - 36x =0;
x(x-6)(x+6)=0;
x₁=0;
x₂=6;
x₃= - 6.
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4)
x² +14x+48 =(x² +8x)+(6x+48) =x(x+8) +6(x+8) =(x+8)(x+6).
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5)
(169³³ +59³)/228 -169*59 =(169+59)(169² -169*59 +59²)/228 -169*59=
=228(169² -169*59 +59²)/228 -169*59 =169² -169*59 +59² -169*59 =
=169² -2*169*59 +59² = (169 -59)² =110² =12100.