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

## The value of an Algebraic Expression

Category : 7th Class

### 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

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

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

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

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

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