Geometric Verification of Standard Square IdentitiesIdentities Involving the Squares and Products of BinomialsAlgebraic Identities

**0:5**[Music]**0:9**hello students welcome to the session on**0:12**algebraic identities so in our previous**0:14**session we have already learned that an**0:16**algebraic equation that holds true for**0:18**any value of the variable in it is**0:21**called as an identity we have a few**0:25**standard algebraic identities that can**0:26**be used for simplifying expressions in**0:29**today's session we will learn about**0:32**three standard identities and verify**0:34**them as well ok so let us begin with the**0:37**four standard identity note which says**0:39**that a plus B the whole square is equals**0:41**to a square plus 2 a B plus B square now**0:45**to verify this identity we write the**0:47**left-hand side as a plus B into a plus B**0:50**now notice that this expression has two**0:54**binomials which are multiplied so by**0:57**using distributive property we further**1:0**get a square plus a B plus B a plus B**1:3**Square here observe carefully the term B**1:6**a and the term a B both are one and the**1:9**same so we add these two terms and we**1:12**get the result as a square plus 2 a B**1:15**plus B Square the left hand side**1:17**expanded gave us the right hand side in**1:20**the identity hence the identity is**1:22**verified this means that we can verify**1:25**the identity for any value of a and any**1:29**value of B to get the values equal on**1:32**both the sides let us now look at the**1:35**second standard algebraic identity which**1:37**says that a minus B the whole square is**1:40**equals to a-square minus 2 AV plus B**1:43**Square now to verify this identity again**1:46**let us write down the left hand side of**1:48**the identity as a minus B into a minus B**1:51**so using distributive property again we**1:54**get the result as a square minus a B**1:57**minus B a plus B Square again we know**2:0**that term B a and term a B both of them**2:3**are one and the same so we add them to**2:6**get the result as a square minus 2 a B**2:9**plus B Square so this verifies our**2:11**identity since the**2:13**pression on the right hand side is**2:14**obtained from the left hand side by**2:16**using multiplication let us now learn**2:19**about the third standard algebraic**2:21**identity which says that a plus B into a**2:24**minus B is equal to a square minus B**2:26**Square**2:27**now using distributive property on the**2:30**left hand side we get a square minus a B**2:33**plus B a minus B squared since the term**2:36**BA is same as the term a be the two**2:39**terms with opposite signs can be**2:42**cancelled and we get a square minus B**2:45**Square which is the right hand side in**2:47**the identity so our third identity is**2:49**also verified now let us quickly recap**2:52**what we have learnt in today's session**2:53**we learned about three identities and we**2:57**also verified them the three identities**2:59**are as follows a plus B the whole square**3:2**is equal to a square plus 2 a B plus B**3:4**square a minus B the whole square is**3:7**equal to a square minus 2 a B plus B**3:10**Square and a plus B into a minus B is**3:13**equal to a square minus B Square that's**3:16**all for now I'll see you in the next**3:18**class till then keep practicing

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$7x=56_{2}âˆ’49_{2}$

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$(xâˆ’y)_{3}âˆ’8x_{3}$

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