Algebraic identity

In this topic algebraic identity we are going to discuss about two formulas which are being used to simplify the terms like in the form (x+a)(x+b). This is a continuation of algebraic identities. We are going to see some of the example problem.After getting clear of using this you can try the worksheet also.We have given this worksheet for the purpose of making practice.If you practice this worksheets it will become easy to face problems in the topic algebra.We will use these formulas in most of the problem.

1. (x+a) (x+b)= x² + x (a+b) + ab

Let us see the explanation of the above formula. For that let us use distributive property.

    (x+a)(x+b) = x(x+b) + a(x+b)

                     = x² + xb + ax +ab

                    =  x² + x(a+b) + ab [by combining like terms]

2. (x-a)(x-b) = x² - x(a+b) + ab

                     Like the above formula we can explain this using distributive property.

    (x-a)(x-b) = x(x-b) - a(x-b)

                    = x² - x(a+b) + ab [by combining like terms]

Algebraic identity-examples

The following examples are based on algebraic identity.

Question 1 :

Expand (3x+5) (3x+8)

Solution:

Here the question is in the form of (x+a)(x+b) . Instead of a we have"5" and instead of b we have "8" . Now we need to apply the formula (x ² + (a+b)x + ab ) and we need to apply those values instead of a and b 

(3x+5) (3x+8)    = (3x)² + (5 + 8) x + (5 x 8) 

                           = 9 x² + 13 x + 40


Question 2 :

Expand (x + 1) (x - 3)

Solution:

Here the question is in the form of (x+a)(x+b) . Instead of a we have"1" and instead of b we have "-3" . Now we need to apply the formula (x² + (a+b)x + ab ) and we need to apply those values instead of a and b 

(x + 1) (x - 3)   = x ² + (1 - 3) x + (1 x (-3)) 

                        = x² - 2 x - 3


 Expand (x-2)(x-3)

Solution:

Here the question is in the form of (x-a)(x-b) . Instead of a we have "2" and instead of b we have "3" . Now we need to apply the formula (x² - (a+b)x + ab ) and we need to apply those values instead of a and b .

(x - 2) (x - 3)   = x ² - (2 + 3) x + (2 x (3)) 

                        = x² - 5 x + 6

Practice problems:

Expand

1. (x+5)(x+1)

2.(x+4)(x-2)

3.(x-2)(x+3)

4.(x-3)(x-7)

Students can try the above problems using the same method we discussed above. If you are having any doubt you can contact us through mail, we will help you to clear your doubts.

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