Exploring Algebraic Identities
Exercise 4.3
Identities
14 questions
Class 9 · Maths
NCERT
Q1 (i)
Find the following squares using one of the above identities.
\(1. (a+b)^2 = a^2 + 2ab + b^2\)
\(2. (a-b)^2 =a^2 - 2ab + b^2\)
\(3. (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\)
Determine which of these identities will make these calculations easier.
\(177^2\)
Q1 (ii)
Find the following squares using one of the above identities.
\(1. (a+b)^2 = a^2 + 2ab + b^2\)
\(2. (a-b)^2 =a^2 - 2ab + b^2\)
\(3. (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\)
Determine which of these identities will make these calculations easier.
\(78^2\)
Q1 (iii)
Find the following squares using one of the above identities.
\(1. (a+b)^2 = a^2 + 2ab + b^2\)
\(2. (a-b)^2 =a^2 - 2ab + b^2\)
\(3. (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\)
Determine which of these identities will make these calculations easier.
\(198^2\)
Q1 (iv)
Find the following squares using one of the above identities.
\(1. (a+b)^2 = a^2 + 2ab + b^2\)
\(2. (a-b)^2 =a^2 - 2ab + b^2\)
\(3. (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\)
Determine which of these identities will make these calculations easier.
\(214^2\)
Q1 (v)
Find the following squares using one of the above identities.
\(1. (a+b)^2 = a^2 + 2ab + b^2\)
\(2. (a-b)^2 =a^2 - 2ab + b^2\)
\(3. (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\)
Determine which of these identities will make these calculations easier.
\(1104^2\)
Q1 (vi)
Find the following squares using one of the above identities.
\(1. (a+b)^2 = a^2 + 2ab + b^2\)
\(2. (a-b)^2 =a^2 - 2ab + b^2\)
\(3. (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\)
Determine which of these identities will make these calculations easier.
\(1120^2\)
Q2 (i)
Factor using suitable identities:
\(16y^2 + 24y + 9\)
Q2 (ii)
Factor using suitable identities:
\(\frac{9}{4}s^2 + 6st + 4t^2\)
Q2 (iii)
Factor using suitable identities:
\(\frac{m^2}{9} + \frac{mk}{3} + \frac{k^2}{4} + 3nk + 2mn + 9n^2\)
Q2 (iv)
Factor using suitable identities:
\(\frac{p^2}{16} − 2 + \frac{16}{p^2} \)
Q2 (v)
Factor using suitable identities:
\(9a^2 + 4b^2 + c^2 − 12ab + 6ac − 4bc \)
Q3 (i)
Expand the following using the identity
\((a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\)
\((p + 3q + 4r)^2\)
Q3 (ii)
Expand the following using the identity
\((a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\)
\((3x − 2y + 4z)^2\)
Q4
Is this an identity?
\((a + b − c)^2 + (a − b + c)^2 + (a − b − c)^2 = 2a^2 + 2b^2 + 2c^2\)