C/m giá trị của các đa thức sau luên ko âm với mọi giá trị của biến

a) x² - 2xy + y² + a² ​

b) x² + 2xy + 2y² ​+ 2y + 1 ​

​c) 9b² - 6b + 4c² ​+ 1

​d) x² + y² + 2x + 6y + 10

a) ma - mb + na - nb - pa +pb

= m(a-b) + n(a-b) - p(a-b) 

= (m+n-p) (a-b)

​b) x^​2​ + ax²​ - y - ay + ax² -cy

= (chữ c ở kia có đúng đề ko?)

c) ax² + 5y - bx² ​+ay + 5x^​2 - by

= a(x^2 +y) - b(x^2 +y) + 5(x^2 +y)​

= (a-b+5) (x^2 +y)

a, (4x+4y)+(by+bx)= 4(x+y)+b(x+y)=(x+y)(4+b)

b, ( 2x²+xy)-(2x+y)= x(2x+y)-(2x+y)=(2x+y)(x-1)

c, (3ax-2bx)-(6ay-4by)= x(3a-2b)-2y(3a-2b)=(3a-2b)(x-2y)

d, (ma+na-pa)-(mb+nb-pb)= a(m+n+p)-b(m+n-p)=(m+n+p)(a-b)

a) 4x+bx+by+4y                b)2x²+xy-2x-y                c)3ax-2bx-6ay+4by                          d)ma-mb+na-nb-pa+pb

=x(4+b)+y(b+4)                 =2x(x-1)+y(x-1)              =3ax-6ay-2bx+4by                            =m(a-b)+n(a-b)-p(a-b)

=(x+y)(b+4)                      =(x-1)(2x+1)                   =3a(x-2y)-2b(x-2y)=(3a-2b)(x-2y)        =(a-b)(m+n-p)

a) Ta có: A = ax + bx + cx + ay + by + cy + az + bz + cz

                  = x.(a+b+c) + y.(a+b+c) + z.(a+b+c)

                  = (a+b+c).(x+y+z) (1)

Lại có: a + b + c = -3 (2)

            x + y + z = -6 (3)

Từ (1) ; (2) ; (3) => A = -3.(-6) = 18

           Vậy A = 18

b) B = ax - bx - cx - ay + by + cy - az + bz +cz

       = x.(a-b-c) - y.(a-b-c) - z.(a-b-c)

       = (a-b-c).(x-y-z)

Lại có: a - b - c = 0 ; x - y - z = 2016

=> B = 0.2016 = 0

Vậy B = 0

a) x²y+xy+x+1= (x²y+xy)+(x+1)=xy(x+10+(x+1)=(x+1)(xy+1)

b) x²-(a+b)x+ab=x²-ax-bx+ab=(x²-ax)-(bx-ab)=x(x-a)-b(x-a)=(x-a)(x-b)

c) ax²+ay-bx²-by=(ax²+ay)-(bx²+by)=a(x²+y)-b(x²+y)=(a-b)(x²+y)

d) ax-2x-a²+2a=(ax-2x)-(a²-2a)=x(a-2)-a(a-2)=(a-2)(x-a)

e) 2x²+4ax+x+2a=(2x²+4ax)+(x+2a)=2x(x+2a)+(x+2a)=(x+2a)(2x+1)

f) x³+ax²+x+a=(x³+ax²)+(x+a)=x²(x+a)+(x+a)=(x²+1)(x+a)

g: Ta có: \(x^4+2x^3-4x-4\)

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

\(=\left(x^2-2\right)\cdot\left(x^2+2x+2\right)\)

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

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

b) \(=xy\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(xy-1\right)\)

c) Đổi đề: \(a^2x+a^2y-7x-7y\)

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

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

e) \(=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)\)

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

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

h) \(=\left(x-y\right)\left(x+y\right)+\left(x+y\right)=\left(x+y\right)\left(x-y+1\right)\)

i) \(=\left(x+1\right)^2-4=\left(x+1-2\right)\left(x+1+2\right)=\left(x-1\right)\left(x+3\right)\)

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

b)\(=xy\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(xy-1\right)\)

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

e)\(=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)\)

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

h)\(=\left(x-y\right)\left(x+y\right)-\left(x-y\right)=\left(x-y\right)\left(x+y-1\right)\)

i)\(=\left(x-1\right)^2-4=\left(x-1-2\right)\left(x-1+2\right)=\left(x-3\right)\left(x+1\right)\)