What is Independent Variable What is Independent Variable In this page we are going to discuss about independent variable. Below you can see how we define independent variable. Independent variable definition :- In an algebraic equation, independent variable means a variable whose values are Independent of changes. In the values of other variables. If y is dependent variable then x is said to be independent variables. For example, take x and y are two variable in the given algebraic equation. Here every value of x is definitely connected with any other value of y, then y value is said to be function of x value is called as an independent variable and y value is called as a “dependent� variable. y values are depending upon the values of x values. Therefore, y = x2 It means y is a dependent variable, Is the square of x value is independent variable. What is an Independent variable ? Know More About What is Standard Form
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In a word, Independent variable means a variable whose it determine the values of other variables. Examples of Independent Variable Below are the examples on Independent Variable Example 1 : Solve the equation 5x+4y +8 =0 Fine the coordinate of vertexes of lines and the x axis in the polynomial. Solution :- Given 5x+4y +8 =0 Substitute x = 0 in the given equation we get, 5(0) +4y +8=0 4y+8=0 Subtract 8 on both sides we get , 4y + 8 - 8 = 0 - 8 4y = -8 Divide 4 on both sides we get y value, y = -2 Therefore the point is (0, -2) Learn More Factor Polynomials
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Difference of Cubes Difference of Cubes n mathematics, factoring is one of the important topic in algebra. Factoring difference of cubes is one of the special cases of factoring. Factoring is the process of splitting a polynomial into products of polynomials of lower degree. Binomials which have same two terms but it contains opposite signs that separates the terms are called as conjugates of each other. Factoring is the process of performing the operation of arithmetic multiplication in reverse. Let us solve some example problems for factoring difference of cubes. Factoring Difference of Cubes Differences of cubes : a3 - b3 = (a - b) (a2 + ab + b2) Examples on Factoring Difference of CubesBack to Top Below are examples on factoring difference of cubes Example 1: Factor the given polynomial expression m3 - 64
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Solution : Given polynomial expression is m3 - 64 It is in the form of difference of cubes m3 - 64 Factor the expression : The first term of the expression can be written as m3 = m . m2 The last term of the expression can be written as 64 = 4 . 42 Now we factor the given expression a3 - b3 = (a - b) (a2 + ab + b2), m3 - 64 = (m -4) (m2 + m (4) + 42) = (m - 4) (m2 + 4m + 16) Ans: m3 - 64 = (m - 4) (m2 + 4m + 16) Example 2: Factor the given polynomial expression a3 - 216 Solution : Given polynomial expression is a3 - 216 It is in the form of difference of cubes a3 - 216 Factor the expression : The first term of the expression can be written as a3 = a . a2 The last term of the expression can be written as 216 = 6 . 62 Now we factor the given expression a3 - b3 = (a – b) (a2 + ab + b2) a3 - 216 = (a - 6) (a2 + a (6) + 62),
= (a - 6) (a2 + 6a + 36)
Ans: a3 - 216 = (a - 6) (a2 + 6a + 36) Read More About Inequalities Worksheet
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