Algebraic Expresssion

Factorization

Factorization is the process of expressing the given algebraic expression as the product of two or more algebraic expression or terms. For example, 2x+5x²  = x(2 + 5x) can be expressed as the product of x and 2 +5x.i.e 2x+5² = x(2 + 5x).When an algebraic expression is the product of two or more expressions, each of these expressions is called a factor of a given expression.In the above examples, x and 2x+5x are the factors of 2x+5x².

Factorization of the expression of the form a²-b²

(i) Take a square piece of paper with one side 'a' unit whose area becomes as sq.units.

(ii) In one of the corners of the square, cut off a small square of side 'b' units. The area of this small squares is so units.

(iii) Let's cut a²-b² diagonally as shown in the figure.

(iv) Arrange two parts to make a rectangle.

Length of the rectangle = (a+b) units

Breagth of the rectangle = (a-b)

Now, area of the rectangle = length × breadth

= (a+b)(a-b)

= a²-b²

∴ Area of rectangle = (a²-b²) sq.unit

∴ a²-b² = (a+b)(a-b)

Things to remember

Some useful formula

• (a+b)² = a²+2ab+b² or (a+b)²+4ab
• (a-b)² = a²-2ab+b² or, (a+b)²-4ab
• a²-b² = (a+b)(a-b)
• a²+b² = (a+b)²-2ab or, (a-b)²+2ab

• It includes every relationship which established among the people.
• There can be more than one community in a society. Community smaller than society.
• It is a network of social relationships which cannot see or touched.
• common interests and common objectives are not necessary for society.

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