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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 3x^{2}y â€“ 2xy^{2} + 2xy for x = 2 and y = â€“2.

Sol:

3x^{2}y â€“ 2xy^{2} + 2xy .

Putting x = 2 and y = â€“2 in the given expression,

3x^{2}y â€“ 2xy^{2} + 2xy

= 3Ã—(2)^{2}Ã—(â€“2) â€“ 2Ã—(2)Ã—(â€“2)^{2} + 2Ã—(2)Ã—(â€“2)

= 3Ã—4Ã—(â€“2) â€“ 4Ã—4 + 4Ã—(â€“2)

= â€“ 24 â€“16 â€“ 8

= â€“ 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 's^{2}'.

If 'l' represents the length and 'b' represents the breadth of a rectangle, then its perimeter is '2(l + b)' and area is 'l Ã— b'.

Area of a triangle with base 'b' and the corresponding altitude 'h' is '$\frac{\text{1}}{\text{2}}$ Ã— base Ã— height'.

Perimeter of an equilateral triangle with the length of the side as 'a' units is '3a'.

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 3x^{2}y â€“ 2xy^{2} + 2xy for x = 2 and y = â€“2.

Sol:

3x^{2}y â€“ 2xy^{2} + 2xy .

Putting x = 2 and y = â€“2 in the given expression,

3x^{2}y â€“ 2xy^{2} + 2xy

= 3Ã—(2)^{2}Ã—(â€“2) â€“ 2Ã—(2)Ã—(â€“2)^{2} + 2Ã—(2)Ã—(â€“2)

= 3Ã—4Ã—(â€“2) â€“ 4Ã—4 + 4Ã—(â€“2)

= â€“ 24 â€“16 â€“ 8

= â€“ 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 's^{2}'.

If 'l' represents the length and 'b' represents the breadth of a rectangle, then its perimeter is '2(l + b)' and area is 'l Ã— b'.

Area of a triangle with base 'b' and the corresponding altitude 'h' is '$\frac{\text{1}}{\text{2}}$ Ã— base Ã— height'.

Perimeter of an equilateral triangle with the length of the side as 'a' units is '3a'.