Phân tích đa thức thành nhân tử
1) x ( x+y ) – 5x -5y
2) 3x^3y – 3xy^3 + x^2 – y^2
3) x^2 – 2xy + y^2 – 2^2
4) (2x + 3)^2 – (x^2 – 6x + 9)
5) x^2 – xy + 5x – 5y
6) x^2 – y^2 + 5x – 5y
7) x^3 + 2x^2 y + xy^2 – 4x
8) xy (x- y) + yz (y- z) + zx (z- x)
9) x^2 +6x + 9 – 25z^2
10) 5x^2 + 5xy – x – y
11) xy (x+ y) + yz (y+ z) + xz (x+ z) + 2xyz
12) 12xy^3 – 18xy^2
13) 9x^2 – 16
14) x^2 – y^2 – 6x + 9
!!! Bạn nào làm được câu nào thì giúp mình với..mình cần gấp 8 câu đầu????????????
Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}1)x\left( {x + y} \right) – 5x – 5y = x\left( {x + y} \right) – 5\left( {x + y} \right) = \left( {x + y} \right)\left( {x – 5} \right)\\2)3{x^3}y – 3x{y^3} + {x^2} – {y^2} = 3xy\left( {{x^2} – {y^2}} \right) + \left( {{x^2} – {y^2}} \right) = \left( {{x^2} – {y^2}} \right)\left( {3xy + 1} \right)\\3)\,{x^2} – 2xy + {y^2} – {2^2} = {\left( {x – y} \right)^2} – {2^2} = \left( {x – y + 2} \right)\left( {x – y – 2} \right)\\4)\,{\left( {2x + 3} \right)^2} – \left( {{x^2} – 6x + 9} \right) = {\left( {2x + 3} \right)^2} – {\left( {x – 3} \right)^2}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {2x + 3 + x – 3} \right)\left( {2x + 3 – x + 3} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \,3x\left( {x + 6} \right)\\5)\,{x^2} – xy + 5x – 5y = x\left( {x – y} \right) + 5\left( {x – y} \right) = \left( {x – y} \right)\left( {x + 5} \right)\\6)\,{x^2} – {y^2} + 5x – 5y = \left( {x – y} \right)\left( {x + y} \right) + 5\left( {x – y} \right) = \left( {x – y} \right)\left( {x + y + 5} \right)\\8)\,xy\left( {x – y} \right) + yz\left( {y – z} \right) + zx\left( {z – x} \right) = {x^2} – {y^2} + {y^2} – {z^2} + {z^2} – {x^2} = 0\\9)\,{x^2} + 6x + 9 – 25{z^2} = {\left( {x + 3} \right)^2} – {\left( {5z} \right)^2} = \left( {x + 3 – 5z} \right)\left( {x + 3 + 5z} \right)\end{array}\)
Các câu còn lại bạn làm tiếp nhé