algebraic expression and an algebraic equation

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 +..

Summary Simultaneous Equations - Finding the solution by the method of substitution. Finding the solution by the method of substitution. (i) Coefficients of one of the variables (say x) in the two equations are made equal, by multiplying them with suitable factors. (ii) By addit..

Linear equations in two variables - A Linear equation is a first degree algebraic expression with one,two or more variables equated to a constant. Graphically a linear equation with one or two variables is a straight line whereas one with ..

If f and g are two functions defined over same domain D, then we have certain set of identities which can be used for solving limits problems with variables like algebraic expressions..

Factorization - If a polynomial can be written as the product of two or more expressions, then each expression is called the factor of the given polynomial.If a polynomial can be written as the product of two or more expressions, then each expression is calle..

The two expressions (LHS and RHS) are equal only for a particular value of the variable (x). These equations are called equations of condition. An equation of condition is generally referred to as an equation..

An equation in a single variable is called a polynomial equation of degree 'n' if it is an equation of the form In other words, an equation is a statement of equality between two algebraic expressions. It is satisfied by a limited numbe..

If a polynomial can be written as the product of two or more expressions, then each expression is called the factor of the given polynomial..

Trinomials - Expressions of the form ax 2 + bx + c are called trinomialsExpressions of the form ax 2 + bx + c are called trinomi..

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..