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 '$\frac{\text{1}}{\text{2}}$ × 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 '$\frac{\text{1}}{\text{2}}$ × base × height'. Perimeter of an equilateral triangle with the length of the side as 'a' units is '3a'.

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