Application of Algebraic Expressions

Algebraic expressions can be used to represent number patterns. 
Ex: Table showing the relation between the number of cones and the number of ice-cream scoops.

Number of cones(n) Number of ice-cream scoops (2n)
    1     2
    2     4
    3     6
    8     16
    15     30


Thus, we can find the value of an algebraic expression if the values of all the variables in the expression are known.
e.g. Find the value of the expression 3x2y – 2xy2 + 2xy for x = 2 and y = –2.

Sol:
3x2y – 2xy2 + 2xy .
Putting x  = 2 and y = –2 in the given expression,
3x2y – 2xy2 + 2xy
= 3×(2)2×(–2) – 2×(2)×(–2)2 + 2×(2)×(–2)
= 3×4×(–2) – 4×4 + 4×(–2)
= – 24 –16 – 8
= – 48.

Formulas and rules such as the perimeter and area for different geometrical figures are written in a concise and general form using simple, and easy-to-remember algebraic expressions.
If 's' represents the side of a square, then its perimeter is '4s' and area is 's2'.
If 'l' represents the length and 'b' represents the breadth of a rectangle, then its perimeter is '2(l + b)' and area is 'l × b'.
Area of a triangle with base 'b' and the corresponding altitude 'h' is ' 1 2  × base × height'.
Perimeter of an equilateral triangle with the length of the side as 'a' units is '3a'.

Summary

Algebraic expressions can be used to represent number patterns. 
Ex: Table showing the relation between the number of cones and the number of ice-cream scoops.

Number of cones(n) Number of ice-cream scoops (2n)
    1     2
    2     4
    3     6
    8     16
    15     30


Thus, we can find the value of an algebraic expression if the values of all the variables in the expression are known.
e.g. Find the value of the expression 3x2y – 2xy2 + 2xy for x = 2 and y = –2.

Sol:
3x2y – 2xy2 + 2xy .
Putting x  = 2 and y = –2 in the given expression,
3x2y – 2xy2 + 2xy
= 3×(2)2×(–2) – 2×(2)×(–2)2 + 2×(2)×(–2)
= 3×4×(–2) – 4×4 + 4×(–2)
= – 24 –16 – 8
= – 48.

Formulas and rules such as the perimeter and area for different geometrical figures are written in a concise and general form using simple, and easy-to-remember algebraic expressions.
If 's' represents the side of a square, then its perimeter is '4s' and area is 's2'.
If 'l' represents the length and 'b' represents the breadth of a rectangle, then its perimeter is '2(l + b)' and area is 'l × b'.
Area of a triangle with base 'b' and the corresponding altitude 'h' is ' 1 2  × base × height'.
Perimeter of an equilateral triangle with the length of the side as 'a' units is '3a'.

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