mathematical Algebraic Identities group 5.pptx

Algebraic identity

1. MATHS ASSIGNMENT ALGEBRAIC IDENTITIES Submitted To: Ms Savita S Submitted By: Aditya Aarav Atharv Shaurya Chaityna

2. ALGEBRAIC IDENTITIES The algebraic equations which are valid for all values of variables in them are called algebraic identities. They are also used for the factorization of polynomials. In this way, algebraic identities are used in the computation of  algebraic expressions  and solving different polynomials.

3. ALGEBRAIC IDENTITIES

4. Identity I : Square of the sum of two terms ( a + b ) 2  = a 2  + 2ab + b 2 Consider a square with side ( a + b ) units We divide the square into four  quadrilaterals  – two rectangles with sides ( a and b ) and two squares with sides a and b. Therefore using area of square formula ( side square )  and area of rectangle  (length* breadth),  we get, The area of the square with side (a + b) units is a 2  + ab + ab + b 2 Therefore, (a + b) 2 = a 2  + 2ab + b 2

5. Identity II :   Square of subtraction of two terms ( a - b ) 2  = a 2  - 2ab + b 2 Consider a square with side a = ( a - b ) + b units We divide the square into three quadrilaterals – two rectangles with sides and a square with sides ( a - b ). Area of square with side a is a 2  = ( a-b ) 2  + b ( a - b) + ab Or, a 2  = ( a-b ) 2  + b a - bb + ab Or, a 2  = ( a-b ) 2  + 2ab - b 2 Or, ( a-b ) 2  = a 2  - 2ab+ b 2

6. Identity III:   Difference of square of two terms ( a + b ) ( a - b )= a 2 - b 2 Consider a square with side a = ( a - b ) + b units We divide the square into three quadrilaterals – two rectangles with sides and a square with sides b . From the figure, the total area of the square with side a can be given by,  Area of square with side a is a 2  = a ( a-b ) + b ( a - b) + b 2 Taking ( a-b ) common in the equation we get, Or, a 2   = ( a + b ) ( a - b) + b 2 Or, a 2 - b 2 = ( a + b ) ( a - b)

7. Identity IV: Multiplication of two algebraic sums ( x + a ) ( x + b ) = x 2  + ( a + b ) x + ab Consider a rectangle with length ( x + b ) units and breadth ( x + a ) units. We divide the rectangle into four quadrilaterals – three rectangles withThe area of rectangle from the figure can be given by  Or, (x + a ) (x + b) = x 2  + xa + xb +ab Or, (x + a ) (x + b) = x 2  + x (a + b ) +ab sides ( x, a ) , ( a, b ), and ( x, b ) . and a square of side x

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