Perfect Square Trinomial Perfect Square Trinomial Perfect Square Trinomial is the product of two binomials but both the binomials are same. When factoring some quadratics which gives identical factors, that quadratics are Perfect Square Trinomial. The general form of perfect square trinomial is (ax-b) 2 =(ax)2-2axb+b2 and (ax+b) 2=(ax)2+ 2axb + b2. In this, the first term and last term of the perfect square are perfect squares and the middle term is 2 times the Square root of first terms times and square root of last terms.Before we explain the straightforward way of factoring perfect square trinomials, we need to define the expression perfect square trinomial Whenever you multiply a binomial by itself twice, the resulting trinomial is called a perfect square trinomial Before we explain the straightforward way of factoring perfect square trinomials, we need to define the expression perfect square trinomial Whenever you multiply a binomial by itself twice, the resulting trinomial is called a perfect square trinomial Know More About Addition Property of Equality Math.Tutorvista.com
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For example, (x + 1) × (x + 1) = x2 + x + x + 1 = x2 + 2x + 1 and x2 + 2x + 1 is a perfect square trinomial Another example is (x − 5) × (x − 5) (x − 5) × (x − 5) = x2 + -5x + -5x + 25 = x2 + -10x + 25 and x2 + -10x + 25 is a perfect square trinomial Example 1 : Factor x2 + 2x + 1 Notice that x2 + 2x + 1 = x2 + 2x + 12 Using x2 + 2x + 12, we see that... the first term is x2 and the base is x the last term is 12 and the base is 1,Put the bases inside parentheses with a plus between them (x + 1),Raise everything to the second power (x + 1)2 and you are done Example 2 : Factor x2 + 24x + 144 But wait before we continue, we need to establish something important when factoring perfect square trinomials. How do we know when a trinomial is a perfect square trinomial? This is important to check this because if it is not, we cannot use the model described above Think of checking this as part of the process when factoring perfect square trinomials We will use example #2 to show you how to check this Start the same way you started example #1 : Notice that x2 + 24x + 144 = x2 + 24x + 122 Using x2 + 24x + 1442, we see that... the first term is x2 and the base is x, the last term is 122 and the base is 12,Now, this is how you check if x2 + 24x + 122 is a perfect square, If 2 times (base of first term) times (base of last term) = second term, the trinomial is a perfect square, If the second term is negative. Learn More Linear Approximation Formula Math.Tutorvista.com
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How to solve Multi Step Equations How to solve Multi Step Equations To solve the linear equations of one variable, we need to solve the equations in such a way that we retain the variable of the equation on one side of the equation and the constant part of the equation is taken to another side of the equation. In this way we get the value of the variable. If the equation is simple equation like x + 5 = 9, such equations can be solved in single step. We can see it in the given equation: We subtract 5 from both the sides we get X + 5- 5 = 9 -5, Or x = 4 Ans But in multi step equations we have to take more than 1 step in order to get the value of the variable. In case the equations have more than one term on both the sides LHS and RHS , it is not possible to solve such equations in just one step. SO more than one step is required to get the solution. We must remember that if the term is shifted from one side of the equal sign to another side, following changes take place: -Positive term becomes negative and the negative term becomes positive.The relation of multiplication becomes relation of division, and the relation of division changes into multiplication. First the addition or subtraction is done and then the operation of multiplication or division is performed.
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- In case, the LCM of 1 side is given, it is first send to another side of the equation, then the addition or subtraction operation is performed. So above equation x + 5 = 9 can be solved by a single step, by taking 5 to R H S. So it becomes x = 9 – 5 x = 4 Ans. Similarly when we have the equations which cannot be solved in single steps are called multi steps equation Solve 3x – 5 = 10, In first step, we will first take 5 from 3x -5 to R H S and get 3 x = 10 + 5, or 3x = 15 Still we need to take another step to get the value of x. We observe that relation between 3 and x is of multiplication, thus to get the value of x, we carry 3 to R H S as a division relation. So we get, x = 15 / 3 Or x = 5 Ans. Similarly we take another example : solve 2x + 5 = x + 9 We bring x from right hand to left and get 2x – x + 5 = 9 or it becomes x + 5 = 9 Now we take 5 to RHS and the sign of 5 becomes -5 x = 9 – 5. Now we find that only x is on the left side and 9 – 5 = 4 is on the right side of the equation. x = 4 Ans Such equations are solved by taking more than 1 steps, so they are called multi steps equations. Read More About Linear Approximation Examples
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