# 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

### Also available in

Class 8 - Standard Identities