1/ 2a + 2b = 2( a + b )

2/ 3a - 6b - 9c = 3( a - 2b - 3c )

3/ 5ax - 15ay + 20a = 5a( x - 3y + 4 )

4/ 3a²x - 6a²y + 12a = 3a( ax - 2ay + 4 )

5/ 4a( x - 5 ) - 2( 5 - x ) = 4a( x - 5 ) + 2( x - 5 ) = ( x - 5 )( 4a + 2 ) = ( x - 5 )2( 2a + 1 )

6. -3a( x - 3 ) + ( 3 - x ) = 3a( 3 - x ) + 1( 3 - x ) = ( 3a + 1 )( 3 - x )

7/ x^m+1 - x^m = x^m( x + 1 )

8/ x^m+2 - x² = x²( x^m - 1 ) 

\(4x^2-\frac{1}{9}\left(y+1\right)^2=\left(2x\right)^2-\left(\frac{1}{3}\left(y+1\right)\right)^2\)

                                       \(=\left(2x-\frac{1}{3}\left(y+1\right)\right)\left(2x+\frac{1}{3}\left(y+1\right)\right)\)

                                       \(=\left(2x-\frac{1}{3}y-\frac{1}{3}\right)\left(2x+\frac{1}{3}y+\frac{1}{3}\right)\)

Ta co \(MP=MB.\sin\widehat{B},MQ=MC.\sin\widehat{C}\)

=> \(MP+MQ=\left(MB+MC\right).\sin\widehat{B}=BC.\sin\widehat{B}=const\)

                                      Bài làm :

Ta có :

(3x+5)(2x-7)

=3x(2x-7) + 5(2x-7)

=6x² - 21x + 10x - 35

= 6x² - 11x +35

Chúc bạn học tốt !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

\(\left(3x+5\right)\times\left(2x-7\right)\)

\(=6x^2-21x+10x-35\)

\(=6x^2-11x-35\)

\(\left(a+b+c\right)^2=3\left(a^2+b^2+c^2\right)_{ }\)

\(a^2+b^2+c^2+2ab+2bc+2ca=3a^2+3b^2+3c^2\)

\(2a^2+2b^2+2c^2-2ab-2bc-2ca=0\)

\(\left(a^2-2ab+b^2\right)+\left(b^2-2bc+c^2\right)+\left(c^2-2ca+a^2\right)=0\)

\(\left(a-b\right)^2+\left(b-c\right)^2+\left(c-a\right)^2=0\)

\(\hept{\begin{cases}a-b=0\\b-c=0\\c-a=0\end{cases}}\)

Do đó  \(P=a^2+\left(a+2\right)\left(2a\right)+2020\)

\(P=a^2+2a^2+4a+2020\)

\(P=3a^2+4a+2020\)

\(3P=9a^2+12a+6060\)

\(3P=\left(3a\right)^2+2.\left(3a\right).2+4+6060-4\)

\(3P=\left(3a+2\right)^2+6056\ge6056\Leftrightarrow3P\ge6056\Leftrightarrow P\ge\frac{6056}{3}\)    Dấu "=" xảy ra khi a = b = c = \(-\frac{3}{2}\)

Vậy P đạt giá trị nhỏ nhất là 6056/3 khi a = b = c = -3/2

Bài làm:

Ta có: \(\frac{9}{4x^2}+\frac{9y^2}{4}-\frac{9y}{2x}\)

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

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

dạ mk cảm ơn bạn De Bruyne nha!

Bài làm:

Ta có: \(2\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\)

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

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

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

\(=3^8-1\)

\(=6561-1=6560\)

                                            Bài làm :

\(\frac{14xy^5\left(2x-3y\right)}{21x^2y\left(2x-3y\right)^2}\)

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

Chúc bạn học tốt !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!