Grade 7 the Multiplication of Expression and an Introduction to Identities Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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(1) Write in How Many Terms Each Simplified Algebraic Expression Has. Then Tick ‘M’ if the Expression is a Monomial, ‘B’ if It is a Binomial and ‘T’ if It is a Trinomial

Table Supporting: 1_Write_in_how_many_terms_each_simplified_algebraic_expression_has_Then_tick_M_if_the_expression_is_a_monomial_B_if_it_is_a_binomial_and_T_if_it_is_a_trinomial
ExpressionNumber of terms after simplificationMonomial/Binomial/Trinomial
(a)
(b)
(c)
(d)

(2) Multiply

(a)

(b)

(C)

(d)

(3) Multiply

(a)

(b)

(C)

(d)

(4) Multiply the Binomials Given

(a)

(b)

(5) Multiply the Binomials Given

(a)

(b)

(6) Write in the Missing Powers, Coefficient, or Terms

(a)

(b)

(7) Write in the Missing Powers, Coefficient, or Terms

(a)

(b)

(8) Use the Identities (A – B) 2 = a2 – 2ab + B2 or (A + B) 2 = a2 + 2ab + B2 to Expand Each of These Expressions

(a)

(b)

(c)

(9) Use the Identities (A – B) 2 = a2 – 2ab + B2 or (A + B) 2 = a2 + 2ab + B2 to Rewrite Each Algebraic Expression as the Square of a Binomial

(a)

(b)

(10) Use the Identities (A – B) 2 = a2 – 2ab + B2 or (A + B) 2 = a2 + 2ab + B2 to Rewrite Each Algebraic Expression as the Square of a Binomial

(a)

(b)

(11) Use the Identity (A + B) (A – B) = a2 – B2 to Match the Expressions in Column a to the Expressions in Column B

Table Supporting: 11_Use_the_identity_a________ba________b________a2________b2_to_match_the_expressions_in_Column_A_to_the_expressions_in_Column_B
Column-AColumn-B
(a)(
(b)
(c)

(12) Use the Identity (X + A) (X + B) = x2 + X (A + B) + Ab to Multiply These Binomials

(a)

(b)

(13) Use an Identity to Answer These Questions

(a)

(b)

(14) Use an Identity to Answer These Questions

(a)

(b)

Answers and Explanations

Answer 1 (A)

  • Given expression:

  • So, Simplest form of given expression
  • There are two number of terms in given algebraic expression as shown below.
Illustration 2 for Answers_and_Explanations
  • Therefore this algebraic expression is Binomial.
Table Supporting: Answers_and_Explanations
ExpressionNumber of terms after simplificationMonomial/Binomial/Trinomial
(a)

Answer 1 (B)

  • Given expression:

  • So, Simplest form of given expression
  • There are two number of terms in given algebraic expression as shown below.
Illustration 3 for Answers_and_Explanations
  • Therefore this algebraic expression is Binomial.
Table Supporting: Answers_and_Explanations
ExpressionNumber of terms after simplificationMonomial/Binomial/Trinomial
(b)

Answer 1 (C)

  • Given expression:

  • So, Simplest form of given expression
  • There are three number of terms in given algebraic expression as shown below.
Illustration 4 for Answers_and_Explanations
  • Therefore this algebraic expression is Trinomial.
Table Supporting: Answers_and_Explanations
ExpressionNumber of terms after simplificationMonomial/Binomial/Trinomial
(C)

Answer 1 (D)

  • Given expression:

  • So, Simplest form of given expression
  • There are three number of terms in given algebraic expression as shown below.
Illustration 5 for Answers_and_Explanations
  • Therefore this algebraic expression is Trinomial.
Table Supporting: Answers_and_Explanations
ExpressionNumber of terms after simplificationMonomial/Binomial/Trinomial
(d)

Answer 2 (A)

  • Given expression:

  • Therefore;

Answer 2 (B)

  • Given expression:

  • Therefore;

Answer 2 (C)

  • Given expression:

  • Therefore;

Answer 2 (D)

  • Given expression:

  • Therefore

Answer 3 (A)

  • Given expression:

  • Therefore

Answer 3 (B)

  • Given expression:

  • Therefore

Answer 3 (C)

  • Given expression:

  • Therefore

Answer 3 (D)

  • Given expression:

  • Therefore

Answer 4 (A)

  • Given binomial expression:

  • Therefore;

Answer 4 (B)

  • Given binomial expression:

  • Therefore;

Answer 5 (A)

Given binomial expression:

  • Therefore;

Answer 5 (B)

Given binomial expression:

  • Therefore;

Answer 6 (A)

  • Given that:

  • So,

  • Now,

  • So,

Answer 6 (B)

  • Given that:

  • So,

  • Now,

  • So,

Answer 7 (A)

  • Given that:

  • So,

  • Now,

  • So,

Answer 7 (B)

  • Given that:

  • So,

  • Now,

  • Therefore;

Answer 8 (A)

  • Given that:

  • We know identities that

  • Compare this identities with given expression; so we have

  • Now, as per the identities

  • Therefore;

Answer 8 (B)

  • Given that:

  • We know identities that

  • Compare this identities with given expression; so we have

  • Now, as per the identities

  • Therefore;

Answer 8 (C)

  • Given that:

  • We know identities that

  • Compare this identities with given expression; so we have

  • Now, as per the identities

  • Therefore;

Answer 9 (A)

  • Given that:

  • We know identities that

  • Compare this identities with given expression; so we have

  • Now,

  • Therefore, the answer is

Answer 9 (B)

  • Given that:

  • We know identities that

  • Compare this identities with given expression; so we have

  • Now,

  • Therefore

Answer 10 (A)

  • Given that:

  • We know identities that

  • Compare this identities with given expression; so we have

  • Now,

  • Therefore

Answer 10 (B)

  • Given that:

  • We know identities that

  • Compare this identities with given expression; so we have

  • Now,

  • Therefore

Answer (11)

  • Identity says that

  • Now for (a) :
  • Compare this with identities,

  • Now,

  • For (b) :
  • Compare this with identities,

  • Now,

  • For (c) :
  • Compare this with identities,

  • Now,

  • Therefore;
Illustration 6 for Answers_and_Explanations

Answer 12 (A)

  • Given expression:

  • Compare this expression with identities

  • So,

  • So,

  • Now using identities;

Answer 12 (B)

  • Given expression:

  • Compare this expression with identities

  • So,

  • So,

  • Now using identities;

Answer 13 (A)

  • Given that:

  • Compare this expression with identities
  • Therefore

  • So,

  • Now,

  • Therefore;

Answer 13 (B)

  • Given that:

  • Compare this expression with identities
  • Therefore

  • So,

  • Now,

  • Therefore;

Answer 14 (A)

  • Given that:

  • Compare this expression with identities:

  • Therefore,

  • So,

  • Now,

  • Therefore;

Answer 14 (B)

  • Given that:

  • Compare this expression with identities:

  • Therefore,

  • So,

  • Now,

  • Therefore;

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