حلول الأسئلة

السؤال

اجمع الحدود الجبرية المتشابهة الآتية:

الحل

$\begin{aligned} - 5 x^{2}, 2 x^{2}, \frac{1}{5} x^{2} \end{aligned}$

$\begin{aligned} - 5 x^{2} + 2 x^{2} + \frac{1}{5} x^{2} \\ = (- 5 + 2 + \frac{1}{5}) x^{2} \\ = \frac{- 25 + 10 + 1}{5} x^{2} = \frac{- 14}{5} x^{2} \end{aligned}$

مشاركة الحل

فايسبوك

واتساب

تيليجرام

طباعة

تدرب وحل التمرينات

اجمع الحدود الجبرية المتشابهة الآتية:

$\begin{aligned} - 5 x^{2}, 2 x^{2}, \frac{1}{5} x^{2} \end{aligned}$

$\begin{aligned} - 5 x^{2} + 2 x^{2} + \frac{1}{5} x^{2} \\ = (- 5 + 2 + \frac{1}{5}) x^{2} \\ = \frac{- 25 + 10 + 1}{5} x^{2} = \frac{- 14}{5} x^{2} \end{aligned}$

$\begin{aligned} \sqrt{169} x^{4} y, 13 x^{4} y, x^{4} y \end{aligned}$

$\begin{aligned} \sqrt{169} x^{4} y + 13 x^{4} y + x^{4} y \\ = & (\sqrt{169} + 13 + 1) x^{4} y \\ = & (13 + 13 + 1) x^{4} y \\ = & 27 x^{4} y \end{aligned}$

$\begin{aligned} \frac{1}{6} xyz, 10 xyz, 20 xyz \end{aligned}$

$\begin{aligned} \frac{1}{6} x y z + 20 x y z = (\frac{1}{6} + 20) x y z \\ = 20 \frac{1}{6} x y z \end{aligned}$

$\begin{aligned} | - 9 | r^{2} v, | - 8 | r^{2} v, | 3 | r^{2} v \end{aligned}$

$\begin{aligned} | - 9 | r^{2} v + | - 8 | r^{2} v + | 3 | r^{2} v \\ = (| - 9 | + | - 8 | + | 3 |) r^{2} v \\ = (9 + 8 + 3) r^{2} v = 20 r^{2} v \end{aligned}$

$\begin{aligned} \frac{3}{2} gh, \frac{6}{5} gh, \frac{1}{4} gh \end{aligned}$

$\begin{aligned} \frac{3}{2} g h + \frac{6}{5} g h + \frac{1}{4} g h \\ = (\frac{3}{2} + \frac{6}{5} + \frac{1}{4}) g h \\ = \frac{30 + 24 + 5}{20} g h = \frac{59}{20} g h \end{aligned}$

$\begin{aligned} \frac{3}{10} {hk}^{2}, \frac{1}{2} h k^{2}, \frac{1}{5} {hk}^{2} \end{aligned}$

$\begin{aligned} \frac{3}{10} H K^{2} + \frac{1}{2} H K^{2} + \frac{1}{5} H K^{2} \\ = (\frac{3}{10} + \frac{1}{2} + \frac{1}{5}) H K^{2} \\ = \frac{3 + 5 + 2}{10} H K^{2} = \frac{10}{10} H K^{2} = H K^{2} \end{aligned}$

جد ناتج طرح الحد الجبري الأول من الحد الجبري الثاني في كل مما يأتي:

$\begin{aligned} 24 z^{2} w, 48 z^{2} w \end{aligned}$

$\begin{aligned} 48 z^{2} w - 24 z^{2} w \\ = & (48 - 24) z^{2} w = 24 z^{2} w \end{aligned}$

$\begin{aligned} 20 r^{2} v, 40 r^{2} v \end{aligned}$

$\begin{aligned} 40 R^{2} V - 20 R^{2} V \\ = & (40 - 20) R^{2} V = 20 R^{2} V \end{aligned}$

$\begin{aligned} 4 xyz, 16 xyz \end{aligned}$

$\begin{aligned} 16 x y z - 4 x y z \\ = & (16 - 4) x y z = 12 x y z \end{aligned}$

$\begin{aligned} | - 9 | ba, | - 20 | ab \end{aligned}$

$\begin{aligned} | - 20 | A B - | - 9 | B A \\ = (| - 20 | - | - 9 |) B A \\ = (20 - 9) B A = 11 B A \end{aligned}$

$\begin{aligned} \frac{1}{5} h^{2} k, \frac{1}{25} {kh}^{2} \end{aligned}$

$(\frac{1}{25} - \frac{1}{5}) H^{2} K = \frac{1 - 5}{25} H^{2} K = \frac{- 4}{25} H^{2} K$

$\begin{aligned} \frac{1}{3} {ab}^{2}, 12 {ab}^{2} \end{aligned}$

$(12 - \frac{1}{3}) A B^{2} = \frac{36 - 1}{3} A B^{2} = \frac{35}{3} A B^{2}$

مشاركة الدرس

فايسبوك

واتساب

تيليجرام

طباعة

السؤال

اجمع الحدود الجبرية المتشابهة الآتية:

الحل

$\begin{aligned} - 5 x^{2}, 2 x^{2}, \frac{1}{5} x^{2} \end{aligned}$

$\begin{aligned} - 5 x^{2} + 2 x^{2} + \frac{1}{5} x^{2} \\ = (- 5 + 2 + \frac{1}{5}) x^{2} \\ = \frac{- 25 + 10 + 1}{5} x^{2} = \frac{- 14}{5} x^{2} \end{aligned}$

تدرب وحل التمرينات

اجمع الحدود الجبرية المتشابهة الآتية:

$\begin{aligned} - 5 x^{2}, 2 x^{2}, \frac{1}{5} x^{2} \end{aligned}$

$\begin{aligned} - 5 x^{2} + 2 x^{2} + \frac{1}{5} x^{2} \\ = (- 5 + 2 + \frac{1}{5}) x^{2} \\ = \frac{- 25 + 10 + 1}{5} x^{2} = \frac{- 14}{5} x^{2} \end{aligned}$

$\begin{aligned} \sqrt{169} x^{4} y, 13 x^{4} y, x^{4} y \end{aligned}$

$\begin{aligned} \sqrt{169} x^{4} y + 13 x^{4} y + x^{4} y \\ = & (\sqrt{169} + 13 + 1) x^{4} y \\ = & (13 + 13 + 1) x^{4} y \\ = & 27 x^{4} y \end{aligned}$

$\begin{aligned} \frac{1}{6} xyz, 10 xyz, 20 xyz \end{aligned}$

$\begin{aligned} \frac{1}{6} x y z + 20 x y z = (\frac{1}{6} + 20) x y z \\ = 20 \frac{1}{6} x y z \end{aligned}$

$\begin{aligned} | - 9 | r^{2} v, | - 8 | r^{2} v, | 3 | r^{2} v \end{aligned}$

$\begin{aligned} | - 9 | r^{2} v + | - 8 | r^{2} v + | 3 | r^{2} v \\ = (| - 9 | + | - 8 | + | 3 |) r^{2} v \\ = (9 + 8 + 3) r^{2} v = 20 r^{2} v \end{aligned}$

$\begin{aligned} \frac{3}{2} gh, \frac{6}{5} gh, \frac{1}{4} gh \end{aligned}$

$\begin{aligned} \frac{3}{2} g h + \frac{6}{5} g h + \frac{1}{4} g h \\ = (\frac{3}{2} + \frac{6}{5} + \frac{1}{4}) g h \\ = \frac{30 + 24 + 5}{20} g h = \frac{59}{20} g h \end{aligned}$

$\begin{aligned} \frac{3}{10} {hk}^{2}, \frac{1}{2} h k^{2}, \frac{1}{5} {hk}^{2} \end{aligned}$

جد ناتج طرح الحد الجبري الأول من الحد الجبري الثاني في كل مما يأتي:

$\begin{aligned} 24 z^{2} w, 48 z^{2} w \end{aligned}$

$\begin{aligned} 48 z^{2} w - 24 z^{2} w \\ = & (48 - 24) z^{2} w = 24 z^{2} w \end{aligned}$

$\begin{aligned} 20 r^{2} v, 40 r^{2} v \end{aligned}$

$\begin{aligned} 40 R^{2} V - 20 R^{2} V \\ = & (40 - 20) R^{2} V = 20 R^{2} V \end{aligned}$

$\begin{aligned} 4 xyz, 16 xyz \end{aligned}$

$\begin{aligned} 16 x y z - 4 x y z \\ = & (16 - 4) x y z = 12 x y z \end{aligned}$

$\begin{aligned} | - 9 | ba, | - 20 | ab \end{aligned}$

$\begin{aligned} | - 20 | A B - | - 9 | B A \\ = (| - 20 | - | - 9 |) B A \\ = (20 - 9) B A = 11 B A \end{aligned}$

$\begin{aligned} \frac{1}{5} h^{2} k, \frac{1}{25} {kh}^{2} \end{aligned}$

$(\frac{1}{25} - \frac{1}{5}) H^{2} K = \frac{1 - 5}{25} H^{2} K = \frac{- 4}{25} H^{2} K$

$\begin{aligned} \frac{1}{3} {ab}^{2}, 12 {ab}^{2} \end{aligned}$

$(12 - \frac{1}{3}) A B^{2} = \frac{36 - 1}{3} A B^{2} = \frac{35}{3} A B^{2}$

حلول الأسئلة

اجمع الحدود الجبرية المتشابهة الآتية:

مشاركة الحل

تدرب وحل التمرينات

اجمع الحدود الجبرية المتشابهة الآتية:

−5x2,2x2,15x2

169x4y,13x4y,x4y

16xyz,10xyz,20xyz

|−9|r2v,|−8|r2v,|3|r2v

32gh,65gh,14gh

310hk2,12hk2,15hk2

جد ناتج طرح الحد الجبري الأول من الحد الجبري الثاني في كل مما يأتي:

24z2w,48z2w

20r2v,40r2v

4xyz,16xyz

|−9|ba,|−20|ab

15h2k,125kh2

13ab2,12ab2

مشاركة الدرس

اجمع الحدود الجبرية المتشابهة الآتية:

تدرب وحل التمرينات

اجمع الحدود الجبرية المتشابهة الآتية:

−5x2,2x2,15x2

169x4y,13x4y,x4y

16xyz,10xyz,20xyz

|−9|r2v,|−8|r2v,|3|r2v

32gh,65gh,14gh

310hk2,12hk2,15hk2

جد ناتج طرح الحد الجبري الأول من الحد الجبري الثاني في كل مما يأتي:

24z2w,48z2w

20r2v,40r2v

4xyz,16xyz

|−9|ba,|−20|ab

15h2k,125kh2

13ab2,12ab2

$\begin{aligned} - 5 x^{2}, 2 x^{2}, \frac{1}{5} x^{2} \end{aligned}$

$\begin{aligned} \sqrt{169} x^{4} y, 13 x^{4} y, x^{4} y \end{aligned}$

$\begin{aligned} \frac{1}{6} xyz, 10 xyz, 20 xyz \end{aligned}$

$\begin{aligned} | - 9 | r^{2} v, | - 8 | r^{2} v, | 3 | r^{2} v \end{aligned}$

$\begin{aligned} \frac{3}{2} gh, \frac{6}{5} gh, \frac{1}{4} gh \end{aligned}$

$\begin{aligned} \frac{3}{10} {hk}^{2}, \frac{1}{2} h k^{2}, \frac{1}{5} {hk}^{2} \end{aligned}$

$\begin{aligned} 24 z^{2} w, 48 z^{2} w \end{aligned}$

$\begin{aligned} 20 r^{2} v, 40 r^{2} v \end{aligned}$

$\begin{aligned} 4 xyz, 16 xyz \end{aligned}$

$\begin{aligned} | - 9 | ba, | - 20 | ab \end{aligned}$

$\begin{aligned} \frac{1}{5} h^{2} k, \frac{1}{25} {kh}^{2} \end{aligned}$

$\begin{aligned} \frac{1}{3} {ab}^{2}, 12 {ab}^{2} \end{aligned}$

$\begin{aligned} - 5 x^{2}, 2 x^{2}, \frac{1}{5} x^{2} \end{aligned}$

$\begin{aligned} \sqrt{169} x^{4} y, 13 x^{4} y, x^{4} y \end{aligned}$

$\begin{aligned} \frac{1}{6} xyz, 10 xyz, 20 xyz \end{aligned}$

$\begin{aligned} | - 9 | r^{2} v, | - 8 | r^{2} v, | 3 | r^{2} v \end{aligned}$

$\begin{aligned} \frac{3}{2} gh, \frac{6}{5} gh, \frac{1}{4} gh \end{aligned}$

$\begin{aligned} \frac{3}{10} {hk}^{2}, \frac{1}{2} h k^{2}, \frac{1}{5} {hk}^{2} \end{aligned}$

$\begin{aligned} 24 z^{2} w, 48 z^{2} w \end{aligned}$

$\begin{aligned} 20 r^{2} v, 40 r^{2} v \end{aligned}$

$\begin{aligned} 4 xyz, 16 xyz \end{aligned}$

$\begin{aligned} | - 9 | ba, | - 20 | ab \end{aligned}$

$\begin{aligned} \frac{1}{5} h^{2} k, \frac{1}{25} {kh}^{2} \end{aligned}$

$\begin{aligned} \frac{1}{3} {ab}^{2}, 12 {ab}^{2} \end{aligned}$