Question

Разложите многочлен на множители
4a^2+12ab+9^2=(2a)^2+2*2a*.....+(....)^2=(2a+.....)^2
n^6-8n^3m^2+16m^4=(....)^2-2*....*....+(8m^2)^2=(.........)^2
49-14x+x^2=
a^2+8ab+16b^2=
m^6+6m^3n+9n^2=
-y^2+10y-25=
7x-14=
-6a^2+4a=
a^2-4b^2=
1/9x^4-y^6=
9a^6-6a^3b-b^2=
x^2+xy+1/4y^2

Answer 1

$\displaystyle4a^2+12a+9^2=(2a)^2+2*(2a)*(3)+3^2=(2a+3)^2\\\\n^6-8n^3m^2+16m^4=(n^3)^2-2*n^3*(4m^2)+(4m^2)^2=(n^3-4m^2)^2\\\\49-14x+x^2=(7)^2-2*7*x+x^2=(7-x)^2\\\\a^2+8ab+16b^2=a^2+2*a*(4b)+(4b)^2=(a+4b)^2\\\\m^6+6m^3*n+(3n)^2=(m^3)^2+2*m^3*(3n)+(3n)^2=(m^3+3n)^2\\\\-y^2+10y-25=-(y^2-2*y*5+5^2)=-(y-5)^2\\\\7x-14=7(x-2)\\\\-6a^2+4a=-2a(3a-2)\\\\a^2-4b^2=(a-2b)(a+2b)\\\\\frac{1}{9}x^4-y^6=(\frac{1}{3}x^2)^2-(y^3)^2=(\frac{1}{3}x^2-y^3)(\frac{1}{3}x^2+y^3)\\\\9a^6-6a^3b-b^2=(3a^3)^2-2*(3a^3)*b-b^2=$

это выражение не формула сокращенного выражения

$\displaystyle9a^6-6a^3b+b^2=(3a^3)^2-2*(3a^3)*b+b^2=(3a^3-b)^2\\\\x^2+xy+(\frac{1}{2}y)^2=x^2+2*x*(\frac{1}{2}y)+(\frac{1}{2}y)^2=(x+\frac{1}{2}y)^2$