Bài 1:

1) 5xy(2x - 3y + 1)

= 10x²y - 15xy² + 5xy

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

= 3x² - 2xy + 3xy - 2y²

= 3x² + xy - 2y²

3) (x - 3)²

= x² - 6x + 9

4) (x + 7)(x - 7)

= x² - 49

5) (7x + 3) + (5x - 1)

= 7x + 3 + 5x - 1

= 12x + 2

6) (x - 1)(2x + 3)

= 2x² + 3x - 2x - 3

= 2x² + x - 3

7) (x + 5)²

= x² + 10x + 25

8) (3x + y)(3x - y)

= 9x² - y²

9) 15xy(4x - 2y + 1)

= 60x²y - 30xy² + 15xy

10) (2x + y)(x - y)

= 2x² - 2xy + xy - y²

= 2x² - xy - y²

11) (2x + 3y)²

= 4x² + 12xy + 9y²

12) (x + 9(x - 9)

= x²- 81

13) x² - 4y²

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

14) 9x² - 16y²

= (3x - 4y)(3x + 4y)

Bài 2:

1) (4x + 3y) + (2x - y)

= 4x + 3y + 2x - y

= 6x + 2y

2) (x + y)(x - y) + y²

= x² - y² + y²

= x²

3) 3x(x - 2y + 1) + 6xy

= 3x² - 6xy + 3x + 6xy

= 3x² + 3x

4) (x - 1)² + 5x

= x² - 2x + 1 + 5x

= x² + 3x + 1

$\displaystyle \begin{array}{{>{\displaystyle}l}} 1) \ 5xy( 2x-3y+1) \ \\ =10x^{2} y-15xy^{2} +5xy\ \\ 2) \ ( x+y)( 3x-2y)\\ =3x^{2} -2xy+3xy-2y^{2}\\ =3x^{2} +xy-2y^{2}\\ 3)( x-3)^{2}\\ =x^{2} -6x+9\\ 4) \ ( x+7)( x-7)\\ =x^{2} -49\ \\ 5) \ ( 7x+3) +( 5x-1)\\ =7x+3+5x-1\\ =12x+2\\ 6) \ ( x-1)( 2x+3)\\ =2x^{2} +3x-2x-3\\ =2x^{2} +x-3\\ 7) \ ( x+5)^{2}\\ =x^{2} +10x+25\\ 8) \ ( 3x+y)( 3x-y)\\ =9x^{2} -y^{2}\\ 9) 15xy( 4x-2y+1)\\ =60x^{2} y-30xy^{2} +15xy\\ 10) \ ( 2x+y)( x-y)\\ =2x^{2} -2xy+xy-y^{2}\\ =2x^{2} -xy-y^{2}\\ 11)( 2x+3y)^{2}\\ =4x^{2} +12xy+9y^{2}\\ 12\ )( x+9)( x-9)\\ =x^{2} -81\ \\ 13.\ x^{2} -4y^{2}\\ =( x-2y)( x+2y)\\ 14) \ 9x^{2} -16y^{2}\\ =( 3x-4y)( 3x+4y) \ \\ Câu\ 2:\ \\ a) \ ( 4x+3y) +( 2x-y)\\ =4x+3y+2x-y\\ =6x+2y\\ b) \ 3x( x-2y+1) +6xy\\ =3x^{2} -6xy+3x+6xy\\ =3x^{2} +3x\\ c) \ ( x+y)( x-y) +y^{2}\\ =x^{2} -y^{2} +y^{2}\\ =x^{2}\\ d) \ ( x-1)^{2} +5x\\ =x^{2} -2x+1+5x\\ =x^{2} +3x+1\ \end{array}$