Lời giải:

$(x^3-2xy+3x^2)(x-2y)=x(x^2-2xy+3x)(x-2y)$

x=67e

a: =x(4x^2+4x+1)

=x(2x+1)^2

b: =(x-y)^2-49

=(x-y-7)(x-y+7)

1, \(4b^2+a^2+4ab=\left(2b+a\right)^2\)

2, \(-49-2a^4+14\sqrt{2}a^2=-\left(2a^4-2.7\sqrt{2}a^2+49\right)=-\left(\sqrt{2}a^2-7\right)^2\)

1: \(a^2+4ab+4b^2=\left(a+2b\right)^2\)

2: \(-49-2a^4+14\sqrt{2a^2}\)

\(=-\left(2a^4-2\cdot\sqrt{2a^2}\cdot7+49\right)\)

\(=-\left(\sqrt{2a^2}-7\right)^2\)

a) Ta có: \(4\left(x-2\right)^2+xy-2y\)

\(=4\left(x-2\right)^2+y\left(x-2\right)\)

\(=\left(x-2\right)\left(4x-8+y\right)\)

b) Ta có: \(x\left(x-y\right)^3-y\left(y-x\right)^2-y^2\left(x-y\right)\)

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

\(=\left(x-y\right)\left[x\left(x-y\right)^2-y\left(x-y\right)-y^2\right]\)

a, x²-x-y²-y = ( x²-y²)-(x+y)=(x-y)(x+y)-(x+y)=(x+y)(x-y-1)

b. x²-2xy+y²-z²= (x-y)² - z²= (x-y-z)(x-y+z)

Ta thấy:
a) \(x^2-x-y^2-y\)
\(=\left(x^2-y^2\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-1\right)\)

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

a, \(2xy-x^2+49-y^2=49-\left(x^2-2xy+y^2\right)\)

                                          \(=7^2-\left(x-y\right)^2\)

                                          \(=\left(7-x+y\right)\left(7+x-y\right)\)

b, \(x^3+2x^2+x=x\left(x^2+2x+1\right)=x\left(x+1\right)^2\)

Bài này dễ mà. Chúc bạn học tốt.

a) \(2xy-x^2+49-y^2\)

\(=49-\left(x^2-2xy+y^2\right)\)

\(=49-\left(x-y\right)^2\)

\(=\left(7+x-y\right)\left(7-x+y\right)\)

b) \(x^3+2x^2+x\)

\(=x\left(x^2+2x+1\right)\)

\(=x\left(x+1\right)^2\)