Algebraic Expresssion
Factorization is the process of expressing the given algebraic expression as the product of two or more algebraic expressions or terms.
Summary
Factorization is the process of expressing the given algebraic expression as the product of two or more algebraic expressions or terms.
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
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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)
Lesson
Algebra
Subject
Compulsory Maths
Grade
Grade 9
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