\(a,\left(-3x^3\right)\left(x^2+5x-\dfrac{1}{3}\right)\)

\(=-3x^5-15x^4+x^3\)

\(b,5p\left(4p^2+7p-3\right)\)

\(=20p^3+35p^2-15p\)

\(c,\left(4y^2-5y+7\right).3y\)

\(=12y^3-15y^2+21y\)

\(d,\left(2x^3-\dfrac{1}{3}x^2+\dfrac{1}{2xy}\right)6x^2y^3\)

\(=12x^5y^3-2x^4y^3+3xy^2\)

Bạn ơi ghi rõ cách làm ra hộ mk dk k

\(A=x^2-xy+\frac{y^2}{4}+\frac{3}{4}\left(y^2-4y+4\right)+2013\)

\(=\left(x-\frac{y}{2}\right)^2+\frac{3}{4}\left(y-2\right)^2+2013\ge2013\)

\(B\) đề thiếu

\(C\) đề sai, dấu của \(y^2\) là âm thì không tồn tại GTNN

\(P=-\left(x^2-2x+1\right)-\left(4y^2+4y+1\right)+7\)

\(=-\left(x-1\right)^2-\left(2y+1\right)^2+7\le7\)

\(2Q=-4x^2-20y^2+12xy+8x-6y+4\)

\(=-\left(4x^2+9y^2+4-12xy-8x+12y\right)-11\left(y^2-\frac{6}{11}y+\frac{36}{121}\right)+\frac{97}{11}\)

\(=-\left(2x-3y-2\right)^2-11\left(y-\frac{3}{11}\right)^2+\frac{97}{11}\le\frac{97}{11}\)

\(\Rightarrow Q\le\frac{97}{22}\)

Sửa lại:

a, x² + 6x + 9

\(x^2+6x+9=x^2+2.x.3+3^2=\left(x+3\right)^2\)
Ely Bang Cái này là HĐT, nhìn cái là ra mà ==

a ) 

\(5x^2-10xy+5y^2-20z^2\)

\(=5\left(x^2-2xy+y^2-4z^2\right)\)

\(=5\left[\left(x-y\right)^2-4z^2\right]\)

b ) 

\(-5x^2-16x-3\)

\(=-5x^2-15x-x-3\)

\(=-5x\left(x+3\right)-\left(x+3\right)\)

\(=\left(-5x-1\right)\left(x+3\right)\)

c ) 

\(x^2-5x+5y-y^2\)

\(=\left(x^2-y^2\right)-5\left(x-y\right)\)

\(=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)\)

\(=\left(x-y\right)\left[\left(x+y\right)-5\right]\)

d ) 

\(3x^2-6xy+3y^2-12z^2\)

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

\(=3\left[\left(x-y\right)^2-4z^2\right]\)

P/s :  Mình bổ sung : 

a ) 

\(=5\left(x-y-2z\right)\left(x-y+2z\right)\)

d ) 

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