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Standard Algebraic Identities

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

Transcript

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