Question

Даю 40 балов .Решительно плиз что сможете .(листик Вариант 4)

Answer 1

$1.1) m^3+125n^3=(m+5n)(m^2+25n^2-5mn)\\1.2) xy^2-16x^3=x(y^2-16x^2)=x(y-4x)(y+4x)\\1.3) -5x^2+30x-45=-5(x^2-6x+9)=-5(x-3)^2$

$1.4) 7xy-42x+14y-84 = 7x(y-6) + 14(y-6) = (7x+14)(y-6) = 7(x+2)(y-6)$

$1.5) 10000-c^4 = (100-c^2)(100+c^2) = (c^2+100)(10-c)(10+c)$

$2) b(b-3)(b+3)-(b-1)(b^2+b+1)=b(b^2-9)-(b^3-1)=1-9b$

$3.1) 81c^2-d^2+9c+d = (9c-d)(9c+d) + (9c+d) = (9c+d)(9c-d+1)$

$3.2) a^2+8ab+16b^2-1=(a+4b)^2-1 = (a+4b-1)(a+4b+1)\\3.3) ax^6-3x^6-ax^3+3x^3=x^3(x^3(a-3)-(a-3))=x^3(x^3-1)(a-3)=x^3(x-1)(x^2+x+1)(a-3)\\3.4) 25-m^2-12mn-36n^2=25-(m+6n)^2=(5-m-6n)(5+m+6n)$

$4.1) 3x^3-108x=0\\3x(x^2-36)=0\\3x(x-6)(x+6)=0\\x \in \{-6,0,6\}$

$4.2) 121x^3-22x^2+x=0\\x(11x-1)^2=0\\x \in \{-\frac{1}{11}, 0, \frac{1}{11}\}$

$4.3) x^3-2x^2-9x+18=0\\x^2(x-2)-9(x-2)=0\\(x-3)(x+3)(x-2)=0\\x \in \[-3,2,3\}$

$5) 3^9-5^3=27^3-5^3=(27-5)(27^2+5^2+27*5)=22(27^2+5^2+27*5)$

6) $(a-b)^2=a^2-2ab+b^2=(a^2+2ab+b^2)-4ab=(a+b)^2-4ab=9^2+4*12=81+48=129$