Question

Многочлен на множители с комбинации различных приемов: 1)6x^5y-24xy^2 2)3a^4b^2+24ab^5 3)0,3y^2-2,7y^6 4)0,1x^4y-2,7xy^4 5)(m+3)^3-8 6)(c-1)^3+27 7)(a-12)^3-125 8)(b+4)^3+64 9)(x^2+1)^2-4x^2 10)(y^2+2y)^2-1 с ! заранее

Answer 1

1)6x^5y-24xy^2=6xy(x^4-4y)
2)3a^4b^2+24ab^5=3ab^2(a^3+8b^3)=3ab^2(a+2b)(a^2+4b^2-2ab)
3)0,3y^2-2,7y^6=0,3y^2(1-9y^4)=0,3y^2(1-3y^2)(1+3y^2)=0,3y^2(1+3y^2)(1-sqrt(3)y)(1+sqrt(3)y))
4)0,1x^4y-2,7xy^4=xy0,1(x^3-27y^3)=0,1xy(x-3y)(x^2+9y^2+3xy)
5)(m+3)^3-8=(m+1)(4+(m+3)^2+2(m+3))=(m+1)(4+9+m^2+6m+6+2m)=
=(m+1)(19+8m+m^2)
6)(c-1)^3+27=(c+2)(c^2+13-5c)
7)(a-12)^3-125=(a-17)(a^2+109-19a)
8)(b+4)^3+64=(b+8)(b^2+16+4b)
9)(x^2+1)^2-4x^2=(x^2-1)^2
10)(y^2+2y)^2-1=(y^2+2y-1)(y^2+2y+1)=(y^2+2y-1)(y+1)^2

Answer 2

$1)6x^5y-24xy^2=6xy(x^4-4y)$
$2)3a^4b^2+24ab^5=3ab^2(a^3+8b^3)=\\3ab^2(a+2b)(a^2-2ab+4b^2)$$3)0,3y^2-2,7y^6=0.3y^2(1-9y^4)=\\0.3y^2(1-3y^2)(1+3y^2)$
$4)0,1x^4y-2,7xy^4=0.1xy(x^3-27y^3)=\\0.1xy(x-3y)(x^2+3xy+9y^2)$
$5)(m+3)^3-8=(m+3-2)((m+3)^2+2m+6+4)=\\(m+1)(m^2+8m+19)$
$6)(c-1)^3+27=(c+2)(c^2-5c+13)$
$7)(a-12)^3-125=(a-17)(a^2+6a-191)$
$8)(b+4)^3+64=(b+8)(b^2+8b+16-4b-16+16=\\(b+8)(b^2+4b+16))$
$9)(x^2+1)^2-4x^2=(x^2+1+2x)(x^2+1-2x)=\\(x+1)(x+1)(x-1)(x-1)$
$10)(y^2+2y)^2-1=(y^2+2y-1)(y^2+2y+1)=\\(y^2+2y-1)(y+1)(y+1)$