algebraic expression npt 3

121x 2 - 25y 2 = (11x) 2 - (5y) 2 = (11x + 5y) (11x - 5y) [Using the identity a 2 -b 2 =(a-b)(a+b)] Factorise: (5a + 6b) 2 - 49b 2 Let x = 5a + 6b Then the given expression = (x) 2 - (7b) 2 = (x + 7b) (x - 7b) Re-substituting the value of x, we get = [(5a + 6b + 7b)] [(5a +..

Equations of condition - Study the following equations: a) 4x + 2 = 14 b) x - 7 = 5 - 2x c) 3a - 8 = a + 12 The equation 4x + 2 = 14 is true only when x = 3, Similarly, x - 7 = 5 - 2x is true only when x = 4, and 3a - 8 = a + 23 is true only when a = 10. The two e..

Identical equations or Identities - Now study the equations given below: a) x + 3 + x + 4 = 2x + 7 2x + 7 = 2x + 7 (By simplification) [ \ any value given to 'x' always satisfies the equation] Similarly, b) (3a + 4) + 2 (a - 1) = 5a + 2 i.e., 5a + 2 = 5a + 2 (By simplification) ..

Summary - If all the terms of the polynomial have a common factor, we take out the common factor and factorise . If all the terms of the polynomial have a common factor, we take out the common factor and factorise . If the polynomial can be expressed as the difference of two squares, we u..

(i) Roster form(i) Roster form (ii) Set builder form (iii) By tables (iv) Arrow diagram (v) By graphs (i) Roster form: The ordered pairs are listed, R = {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5)} Where A = {1, 2, 3, 4, 5} and R means 'is twice' in A x A xRy means x = 2y. (i) x = ..

f : {(x, y) : y = 4x + 5} where x belongs to real numbers. (iv) A table. The following table represents first to fifth rank holders of a class. (vi) An algebraic formula. We can use an algebraic formula to represent a function {(x, y) : f(x) = x 2 + 3, x I} Do..

When the coefficient of the highest power is 1. i.e., ax 2 bx c, when a = 1 and b and c are integers. When two binomials are multiplied the product is a trinomial. Thus (x + 4) (x + 5) = x 2 + 9x + 20 (1) (x - 4) (x - 5) = x 2 - 9x + 20 (2) In this chapter we try to express ..

A formula is formed by using:A formula is formed by using: (a) mathematical symbols and variables (b) given conditions, and (c) simplification. Some well known formulae are listed below: Area of a rectangle A = l x b A = Area l = Length b = Breadth Perimeter of a rectangle P = 2(l + b) P = Perimete..

(5y) + (5y) 2 = x 2 - 10xy + 25y 2 Find algebraically the value of 205 2 . 205 2 = (200 + 5) 2 = (200) 2 + 2 (200) (5) + (5) 2 = 40000 + 2000 + 25 = 42025 If the expression 36x 2 + Kx + 25 is a perfect square, find K. Middle term of the given expression..

For each shaded area, state the inequalities, which are true. a..