question_answer 2)

(i) Identify the terms and `their factors in the following expressions. Show the terms and factors by tree diagrams: (a) \[x-3\]                            (b) \[1+x+{{x}^{2}}\]                      (c) \[y-{{y}^{3}}\]                             (d) \[5x{{y}^{2}}+7{{x}^{2}}y\] (e) \[-ab+2{{b}^{2}}-3{{a}^{2}}\] (ii) Identity terms and factors in the expressions given below: (a) \[-4x+5\]                       (b) \[-4x+5y\]                    (c) \[5y+3{{y}^{2}}\]                       (d) \[xy+2{{x}^{2}}{{y}^{2}}\]        (e) \[pq+q\]                       (f) \[1.2ab-2.4b+3.6a\]  (g) \[\frac{3}{4}x+\frac{1}{4}\]                   (h) \[0.1{{p}^{2}}+0.2{{q}^{2}}\]                

Answer:

                (i) (a) \[x-3\]                              Terms: \[x;-3\]         Factor: \[x;-3\]         (b) \[\mathbf{1+x+}{{\mathbf{x}}^{\mathbf{2}}}\]         Terms: \[1\,\,;\,\,x\,\,;\,\,{{x}^{2}}\]         Factors: \[1;x;x,x\] (c) \[\mathbf{y-}{{\mathbf{y}}^{\mathbf{3}}}\] Terms: \[y;-{{y}^{3}}\] Factors: \[y:-1,y,y,y\] (d) \[\mathbf{5x}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{+7}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{y}\] Terms: \[5x{{y}^{2}}:7{{x}^{2}}y\] Factors: \[5,x,y,y;7,x,x,y\] (e) \[\mathbf{-ab+2}{{\mathbf{b}}^{\mathbf{2}}}\mathbf{-3}{{\mathbf{a}}^{\mathbf{2}}}\] Terms: \[-ab;2{{b}^{2}};-3{{a}^{2}}\] Factor: \[-1,a,b;2,b,b;-3,a,a\] (ii) (a) \[\mathbf{-4x+5}\]                            Terms: \[-4x;5\] Factors: \[-1,4,x;5\] (b) \[\mathbf{-4x+5y}\] Terms: \[-4x;5y\] Factors: \[-4,x;5,y\] (c) \[\mathbf{5y+3}{{\mathbf{y}}^{\mathbf{2}}}\]                          Terms: \[5y;3{{y}^{2}}\]                                Factory: \[5,y;3,y,y\]      (d) \[\mathbf{xy+2}{{\mathbf{x}}^{\mathbf{2}}}{{\mathbf{y}}^{\mathbf{2}}}\] Terms: \[xy;2{{x}^{2}}{{y}^{2}}\] Factory: \[x,y;2,x,x,y,y\] (e) \[\mathbf{pq+q}\]                   Terms: \[pq;q\]                 Factors: \[p,q;q\]                             (f) \[\mathbf{1}\mathbf{.2ab-2}\mathbf{.4b+3}\mathbf{.6a}\] Terms: \[1.2ab;-2.4b;3.6a\] Factors: \[1.2,a,b;-2.4,b;3.6,a\] (g) \[\frac{\mathbf{3}}{\mathbf{4}}\mathbf{x+}\frac{\mathbf{1}}{\mathbf{4}}\]                             Terms: \[\frac{3}{4}x;\frac{1}{4}\]                            Factors: \[\frac{3}{4},x;\frac{1}{4}\]                         (h) \[\mathbf{0}\mathbf{.1}{{\mathbf{p}}^{\mathbf{2}}}\mathbf{+0}\mathbf{.2}{{\mathbf{q}}^{\mathbf{2}}}\] Terms: \[0.1{{p}^{2}};0.2{{q}^{2}}\] Factor: \[0.1p,p;0.2,q,q\].