Question

I : Phân tích đa thức thành nhân tử

a) a^2+b^2+2ab+2a+2b+1

b)3x(x-2y)+6y(2y-x)

c)16xy+4y^2-9+16x^2

d) x^4+64y^8

3)3x^2-7x+2

Answer 1

a)

\(a^2+b^2+2ab+2a+2b+1\)

\(=(a^2+2ab+b^2)+(2a+2b)+1\)

\(=(a+b)^2+2(a+b)+1^2=(a+b+1)^2\)

b)

\(3x(x-2y)+6y(2y-x)\)

\(=3x(x-2y)-6y(x-2y)=(3x-6y)(x-2y)=3(x-2y)(x-2y)\)

\(=3(x-2y)^2\)

Answer 2

c)

\(16xy+4y^2-9+16x^2\)

\(=(16x^2+16xy+4y^2)-9\)

\(=(4x+2y)^2-3^2=(4x+2y-3)(4x+2y+3)\)

d)

\(x^4+64y^8=(x^2)^2+(8y^4)^2=(x^2)^2+(8y^4)^2+2.x^2.8y^4-2x^2.8y^4\)

\(=(x^2+8y^4)^2-16x^2y^4=(x^2+8y^4)^2-(4xy^2)^2\)

\(=(x^2+8y^4-4xy^2)(x^2+8y^4+4xy^2)\)

e)

\(3x^2-7x+2=3x^2-6x-x+2=(3x^2-6x)-(x-2)\)

\(=3x(x-2)-(x-2)=(3x-1)(x-2)\)