Algebraic Expressions and Identities
Summary (Concept details)
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Terms, Factors and Coefficients
Monomials, Binomials and Polynomials
Like and unlike terms
Addition, subtraction of algebraic expressions
Introduction on Multiplication of Algebraic Expressions
Multiplying a Monomial by a Monomial
Multiplying a Monomial by a Polynomial
Multiplying a Polynomial by a Polynomial
Standard Identities
Application of standard identities in problem solving
Level Wise Question:
Level 1
Question 1: Frame the algebraic expression in each of
the following cases.
(i) Sum of x and 9
(ii) 2 subtracted from p
(iii) 5 times m 4
(iv) take away 6 times y, from x
Question 2: Find 4x X 5y X 7z
Level 2
Question 1: Give two examples of situations, where we
may need to multiply algebraic expressions.( Hint: think of
speed and time; interest to be paid, the principal and the
rate of interest; etc.)
Question 2: What is an identity?
Level 3
Question 1: Verify Identity (IV) for a=2, b=3 and x=5.
Question 2: Put -b in place of b in Identity (I). Do you
get Identity (II)?
Activity: [Group activity (on chart paper) or individual
activity (in activity book)]
Prove the identity (a+b)2 = a2+b2+2ab, using geometrical
figures.
Objective: To visualise and reinforce the concept of
identities.
Method:
Step 1: Draw a square ABCD and divide it into two squares
and two rectangles.
Step 2: Let AE denote ‘a’ units and EB denote ‘b’ units.
Therefore AB = (a+b) units
Step 3: Shade the two squares in one colour and the two
rectangles in another colour.
Area of Square ABCD = Sum of areas of shaded portions
(i.e) (a+b)2 = a2+b2+2ab
Home assignment:
Prove the identity II by finding the area of a square with the
measure of the side (a-b) units. The following diagram gives a
hint to prove the same.