\(x^3+3x^2y+3xy^2+y^3-x-y=\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left[\left(x+y\right)^2-1\right]=\left(x+y\right)\left(x+y+1\right)\left(x+y-1\right)\)

Ta có : \(x^3+3x^2y+3xy^2+y^3-x-y.\)

\(=\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)

Trả lời:

\(27a^2b^2-18ab+3\)

\(=3\left(9a^2b^2-6ab+1\right)\)

\(=3\left[\left(3ab\right)^2-2.3ab.1+1^2\right]\)

\(=3\left(3ab-1\right)^2\)

bằng phương pháp dùng hằng đẳng thức ak??

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x² - 7xy + y²

= (x² - 2xy + y²) - 5xy

= (x - y)² - 5xy

còn lại bn xem thu gọn được ko thì làm nhé!!

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a: \(27a^2b^2+18ab+3\)

\(=3\left(9a^2b^2+6ab+1\right)\)

\(=3\left\lbrack\left(3ab\right)^2+2\cdot3ab\cdot1+1^2\right\rbrack\)

\(=3\left(3ab+1\right)^2\)

b: \(5x^2-y+5xy-x\)

=5x(x+y)-(x+y)

=(x+y)(5x-1)

c: \(2x^3y^2-8x^3-12x^2y-6xy^2-y^3+x^2y^3\)

\(=x^2y^2\left(2x+y\right)-\left(2x+y\right)^3\)

\(=\left(2x+y\right)\left\lbrack x^2y^2-\left(2x+y\right)^2\right\rbrack\)

=(2x+y)(xy-2x-y)(xy+2x+y)

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

\(=\left(a+b\right)^2+2\left(a+b\right)+1=\left[\left(a+b\right)+1\right]^2=\left(a+b+1\right)^2\)

b) K phân tích dc.

giúp với ạ

Trả lời:

a, \(27a^2b^2-18ab+3=3\left(9a^2b^2-6ab+1\right)=3\left(3ab-1\right)^2\)

b, \(x^2+2xy+y^2-xz-yz\)

\(=\left(x^2+2xy+y^2\right)-z\left(x+y\right)\)

\(=\left(x+y\right)^2-z\left(x+y\right)\)

\(=\left(x+y\right)\left(x+y-z\right)\)

c, \(a^4+a^3-a^2-a\)

\(=\left(a^4+a^3\right)-\left(a^2+a\right)\)

\(=a^3\left(a+1\right)-a\left(a+1\right)\)

\(=a\left(a+1\right)\left(a^2-1\right)\)

\(=a\left(a+1\right)\left(a-1\right)\left(a+1\right)\)

\(=a\left(a+1\right)^2\left(a-1\right)\)

d, \(a^3-b^3+2b-2a\)

\(=\left(a^3-b^3\right)-\left(2a-2b\right)\)

\(=\left(a-b\right)\left(a^2+ab+b^2\right)-2\left(a-b\right)\)

\(=\left(a-b\right)\left(a^2+ab+b^2-2\right)\)

=a²(64x³-27y³)

=a²[(4x)³-(3y)³]

=a²(4x-3y)[(4x)²+4x.3y+(3y)²]

=a²(4x-3y)(16x²+12xy+9y²)

x.x-2.x-1-y.y

\(\) \(x^2-2x-1-y^2=(x^2-2x+1)-2+y^2=(x-1)^2+y^2-2=((x-1)-y)((x-1)+y)-2=(x-1-y)(x+1+y)+2\)