7th Class Mathematics Algebraic Expressions The value of an Algebraic Expression

     The value of an Algebraic Expression  

Step 1:   If possible simplify the given algebraic expression.  

Step 2:   Replace variable with given numerical value.  

Step 3:   Simplify it.  

Find the value of \[\frac{{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz}{{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-xy-yz-zx},\] lf \[x=1,y=2\] and \[z=-1.\]

(a) 24                                                    

(b) 14

(c) 7                                                      

(d) 2

(e) None of these  

Answer: (d)

Explanation

\[\frac{{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz}{{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-xy-yz-zx}=\frac{(x+y+z+)({{x}^{2}}+{{y}^{2}}+{{z}^{2}}-xy-yz-zx)}{({{x}^{2}}+{{y}^{2}}+{{z}^{2}}-xy-yz-zx)}\]

\[=(x+y+z).\] Now putting the values of \[x,\text{ }y\]and \[z\] we get = 2  

  Find the value of \[4\text{ }xy\text{(}x-y\text{)}-6{{x}^{2}}\text{(}y-{{y}^{2}}\text{)}-3{{y}^{2}}(2{{x}^{2}}-x)+2xy(x-y)\] for \[x=5\]and \[y=13.\]

(a) - 195                              

(b) 2535

(c) - 2535                                            

(d) 215

(e) None of these  

Answer: (c)  

Explanation

\[4xy(x-y)-6{{x}^{2}}(y-{{y}^{2}})-3{{y}^{2}}(2{{x}^{2}}-x)+2xy(x-y)\]\[4{{x}^{2}}y-4x{{y}^{2}}-6{{x}^{2}}y+6{{x}^{2}}{{y}^{2}}-6{{y}^{2}}{{x}^{2}}+3x{{y}^{2}}+2{{x}^{2}}y-2x{{y}^{2}}\]

After simplification, we get \[-\text{ }3x{{y}^{2}}=-3\times 5\times 13\times 13=-2535\]    

  The value of A, B, C, D, E, F, G, H and I for which \[(ABC)\times (DEF)=GHI\]                

(a) (6, 5, 7, 8, 2, 6, 1, 8, 4, 0)         

(b) (7, 9, 5, 2, 6, 4, 8, 4, 0)

(c) (4, 6, 7, 8, 5, 7, 0, 8, 9)              

(d) (1, 0, 3, 7, 8, 4, 2, 1, 0)                

(e) None of these  

Answer: (d)

Explanation

If we put the value of A, B, C, D, E, F, G, H and I from option D in the left hand side and right hand side of given expression, then it becomes zero.  

  Find the value of \[3{{x}^{3}}y+4{{x}^{y}}+2{{y}^{x}},\] if \[x=2\]\[x=2\]and \[y=-2.\] 

(a) - 39                                                

(b) 39

(c) 13                                                    

(d) Cannot be determined

(e) None of these  

Answer: (a)  

  Find the value of \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ca,\]if \[a=2b=-2\]and \[c=1.\]

(a) 12                                                    

(b) 1

(c) 13                                                    

(d) 7

(e) None of these

Answer: (d)  

  Which one of the following options is the correct value or the expression \[\frac{axy+byz+cxy}{ax+by+cz+1},\] if \[a=1,b=2,c=-1,x=-1,y=2,z=3?\]  

(a) 12                                                    

(b) 10

(c) 13                                                    

(d) 11

(e) None of these                                

Answer: (a)