1:

a: \(\left(x+y+z\right)^2=x^2+y^2+z^2+2xy+2zx+2yz\)

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

c: \(\left(x-y-z\right)^2=x^2+y^2+z^2-2xy-2xz+2yz\)

Bài 2: tất cả đều ở dạng tích rồi mà

Bài 1:

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

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

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

d) \(\left(a^2-2a+3\right)\left(a^2+2a+3\right)=9-\left(a^2-2a\right)^2\)

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

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

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

Bài 2 :

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

b) \(\left(x+y+z\right)^2=\left(x+y+z\right)\left(x+y+z\right)=x^2+xy+xz+yx+y^2+yz+zx+zy+z^2=x^2+2xy+2yz+2xz+y^2+z^2\)

c) \(\left(x-y+z\right)^2=\left(x-y+z\right)\left(x-y+z\right)=x^2-xy+xz-xy+y^2-yz+xz-yz+z^2=x^2+y^2+z^2-2xy+2xz-2yz\)d) \(\left(x-2y\right)\left(x^2+2xy+4y^2\right)=\left(x-2y\right)^3\)

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

Bài 1:

a) -16 +(x-3)²

<=> (x-3)²-16

<=> (x-3)² -4²

<=> (x-3-4)(x-3+4)

<=> (x-7)(x+1)

b) 64+16y+y²

<=> y² + 2.8.y + 8²

<=> (y+8)²

c) \(\dfrac{1}{8}-8x^3\)

\(\Leftrightarrow\left(\dfrac{1}{2}\right)^3-\left(2x\right)^3\)

\(\Leftrightarrow\left(\dfrac{1}{2}-2x\right)\left(\dfrac{1}{4}+x+4x^2\right)\)

d)\(x^2-x+\dfrac{1}{4}\)

\(\Leftrightarrow x^2-2.\dfrac{1}{2}.x+\left(\dfrac{1}{2}\right)^2\)

\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2\)

e) x⁴ + 4x² + 4

<=> (x²)² + 2.2.x² +2²

<=> (x² + 2)²

g)\(8x^3+60x^2y+150xy^2+125y^3\)

\(\Leftrightarrow\left(2x+5y\right)^3\)

2:

-8x^6-12x^4y-6x^2y^2-y^3

=-(8x^6+12x^4y+6x^2y^2+y^3)

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

3:

=(1/3)^2-(2x-y)^2

=(1/3-2x+y)(1/3+2x-y)

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

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

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

b: \(\left(x-3\right)^2-2\left(x^2-9\right)+\left(x+3\right)^2\)

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

=36

c: \(\left(a^2-b^2\right)^2-\left(a+b^2\right)^2\)

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

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

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

a) Ta có:

(x+y+z)(x-y-z) = x^2 -xy -xz +yx- y^2 -yz+zx -zy -z^2

=x^2 - y^2 - 2yz - z^2.

b) Ta có: (x-y+z)(x+y+z) = x^2 +xy+xz -yx-y^2 -yz +zx+zy +z^2

=x^2 +2xz- y^2 +z^2.

c) Ta có: -16 + (x-3)^2 = -16 + ( x^2-6x+9)

= -16 + x^2 - 6x + 9

= x^2 - 6x - 7.

\(a,\left(x+y+z\right)\left(x-y-z\right)\)

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

\(=x^2-xy-xz+xy-y^2-yz+xz-yz-z^2\)

\(=x^2-y^2-2yz-z^2\)

\(b,\left(x-y+z\right)\left(x+y+z\right)\)

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

\(=x^2+xy+xz-xy-y^2-yz+xz+yz+z^2\)

\(=x^2+2xz-y^2+z^2\)

\(c,-16+\left(x-3\right)^2\)

\(=-16+x^2-6x+9\)

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