Đáp án:

\(\begin{array}{l}
14,\\
\left( {2x - 1} \right)\left( {2x + 3} \right)\\
15,\\
\left( {4x + 3} \right)\left( {x + 3} \right)\\
16,\\
\left( {x - 2} \right)\left( {4x + 1} \right)\\
17,\\
\left( {x + 1} \right)\left( {3x - 2} \right)\\
18,\\
\left( {3x + 2} \right)\left( {2x + 1} \right)\\
19,\\
\left( {x - 4} \right)\left( {5x + 2} \right)\\
20,\\
\left( {x - 2y} \right)\left( {x + y} \right)\\
21,\\
\left( {x - y} \right)\left( {x - 2y} \right)\\
22,\\
\left( {x - 2y} \right).\left( {2x + y} \right)\\
23,\\
\left( {x + 2y} \right)\left( {2x + y} \right)\\
24,\\
2.\left( {x - y} \right)\left( {x + 2y} \right)
\end{array}\)

Giải thích các bước giải:

\(\begin{array}{l}
14,\\
4{x^2} + 4x - 3\\
 = \left( {4{x^2} - 2x} \right) + \left( {6x - 3} \right)\\
 = 2x.\left( {2x - 1} \right) + 3.\left( {2x - 1} \right)\\
 = \left( {2x - 1} \right)\left( {2x + 3} \right)\\
15,\\
4{x^2} + 15x + 9\\
 = \left( {4{x^2} + 3x} \right) + \left( {12x + 9} \right)\\
 = x\left( {4x + 3} \right) + 3.\left( {4x + 3} \right)\\
 = \left( {4x + 3} \right)\left( {x + 3} \right)\\
16,\\
4{x^2} - 7x - 2\\
 = \left( {4{x^2} - 8x} \right) + \left( {x - 2} \right)\\
 = 4x.\left( {x - 2} \right) + \left( {x - 2} \right)\\
 = \left( {x - 2} \right)\left( {4x + 1} \right)\\
17,\\
3{x^2} + x - 2\\
 = \left( {3{x^2} + 3x} \right) + \left( { - 2x - 2} \right)\\
 = 3x\left( {x + 1} \right) - 2.\left( {x + 1} \right)\\
 = \left( {x + 1} \right)\left( {3x - 2} \right)\\
18,\\
6{x^2} + 7x + 2\\
 = \left( {6{x^2} + 4x} \right) + \left( {3x + 2} \right)\\
 = 2x.\left( {3x + 2} \right) + \left( {3x + 2} \right)\\
 = \left( {3x + 2} \right)\left( {2x + 1} \right)\\
19,\\
5{x^2} - 18x - 8\\
 = \left( {5{x^2} - 20x} \right) + \left( {2x - 8} \right)\\
 = 5x.\left( {x - 4} \right) + 2.\left( {x - 4} \right)\\
 = \left( {x - 4} \right)\left( {5x + 2} \right)\\
20,\\
{x^2} - xy - 2{y^2}\\
 = \left( {{x^2} - 2xy} \right) + \left( {xy - 2{y^2}} \right)\\
 = x\left( {x - 2y} \right) + y\left( {x - 2y} \right)\\
 = \left( {x - 2y} \right)\left( {x + y} \right)\\
21,\\
{x^2} - 3xy + 2{y^2}\\
 = \left( {{x^2} - xy} \right) + \left( { - 2xy + 2{y^2}} \right)\\
 = x\left( {x - y} \right) - 2y\left( {x - y} \right)\\
 = \left( {x - y} \right)\left( {x - 2y} \right)\\
22,\\
2{x^2} - 3xy - 2{y^2}\\
 = \left( {2{x^2} - 4xy} \right) + \left( {xy - 2{y^2}} \right)\\
 = 2x.\left( {x - 2y} \right) + y.\left( {x - 2y} \right)\\
 = \left( {x - 2y} \right).\left( {2x + y} \right)\\
23,\\
2{x^2} + 5xy + 2{y^2}\\
 = \left( {2{x^2} + 4xy} \right) + \left( {xy + 2{y^2}} \right)\\
 = 2x.\left( {x + 2y} \right) + y\left( {x + 2y} \right)\\
 = \left( {x + 2y} \right)\left( {2x + y} \right)\\
24,\\
2{x^2} + 2xy - 4{y^2}\\
 = 2.\left( {{x^2} + xy - 2{y^2}} \right)\\
 = 2.\left[ {\left( {{x^2} - xy} \right) + \left( {2xy - 2{y^2}} \right)} \right]\\
 = 2.\left[ {x.\left( {x - y} \right) + 2y.\left( {x - y} \right)} \right]\\
 = 2.\left( {x - y} \right)\left( {x + 2y} \right)
\end{array}\)

Đáp án:

`14. 4x^2+4x-3`

`= 4x^2-2x+6x-3`

`= (2x-1)(2x+3)`

`15. 4x^2+15x+9`

`= 4x^2+12x+3x+9`

`= 4x(x+3)+3(x+3)`

`= (x+3)(4x+3)`

`16. 4x^2-7x-2`

`= 4x^2-8x+x-2`

`= 4x(x-2)+(x-2)`

`= (x-2)(4x+1)`

`17. 3x^2+x-2`

`= 3x^2+3x-2x-2`

`= 3x(x+1)-2(x+1)`

`= (x+2)(3x-2)`

`18. 6x^2+7x+2`

`= 6x^2+4x+3x+2`

`= 2x(3x+2)+(3x+2)`

`= (3x+2)(2x+1)`

`19. 5x^2-18x-8`

`= 5x^2-20x+2x-8`

`= 5x(x-4)+2(x-4)`

`= (x-4)(5x+2)`

`20. x^2-xy-2y^2`

`= x^2-2xy+xy-2y^2`

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

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

`21. x^2-3xy+2y^2`

`= x^2-2xy-xy+2y^2`

`= x(x-2y)-y(x-2y)`

`= (x-2y)(x-y)`

`22. 2x^2-3xy-2y^2`

`= 2x^2-4xy+xy-2y^2`

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

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

`23. 2x^2+5xy+2y^2`

`= 2x^2+4xy+xy+2y^2`

`= 2x(x+2y)+y(x+2y)`

`= (x+2y)(2x+y)`

`24. 2x^2+2xy-4y^2`

`= 2(x^2+xy-2y^2)`

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