# Grade 8 Identities Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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## (1) Use the Identities to Expand the Following Algebraic Expressions

(a)

(b)

(c)

## (2) Use the Identities to Expand the Following Algebraic Expressions

(a)

(b)

## (3) Use the Identities to Rewrite Each Algebraic Expression as a Square of a Binomial

(a)

## (4) Use the Identities to Rewrite Each Algebraic Expression as a Square of a Binomial

(a)

## (5) Use the Identities to Answer These Questions

(a)

## (6) Use the Identities to Answer These Questions

(a)

## (7) Use the Identities to Answer These Questions

(a) Find , when

## (8) Use the Correct Identity to Solve the Following Problems

(a)

(b)

## (9) Use the Correct Identity to Solve the Following Problems

(a)

(b)

## (10) Use the Identities to Expand the Following Algebraic Expressions

(a)

(b)

## (11) Use the Identities to Answer These Questions

(a) If , find

(b) If , find the value of

## (12) Use the Identities to Answer These Questions

(a) If find the value of

## (13) Use the Identities to Answer These Questions

(a) If , find the value of

## Answers and Explanations

### Answer 1 (A)

- Here given algebraic expression is,

- Hence
- Now,

### Answer 1 (B)

- Here given algebraic expression is,

- Hence
- Now,

### Answer 1 (C)

- Here given algebraic expression is,

- Hence
- Now,

### Answer 2 (A)

- Here given algebraic expression is,

- Hence
- Now,

### Answer 2 (B)

- Here given algebraic expression is,

- Hence
- Now,

### Answer 3 (A)

- Given algebraic expression is;

- Now compare this algebraic expression with So we have,

- Hence from above ,

- Hence,

- So, algebraic expressions as a square of a binomial

### Answer 4 (A)

- Given algebraic expression is;

- Now compare this algebraic expression with So we have,

- Hence from above ,

- Hence,

- So, algebraic expressions as a square of a binomial

### Answer 5 (A)

- To answer this with the use identities we first consider
- Answer of above will multiply with remaining expression for further solution
- Hence , first part

- Now compare our algebraic expression with identities
- Hence,

- From above,
- Hence,

- Now, second part

- Now compare our algebraic expression with identities
- Hence,
- From above
- Hence,

- Hence,

### Answer 6 (A)

- Now we know the identities that,

- Hence

- Put the value of in above equation

### Answer 7 (A)

- Given values are,

- Now we know the identities that,

- Hence,

- Put the value in above equation,

### Answer 8 (A)

- Given problem,
- We know the identities that,

- Compare our equation with identities expression than,

- Hence
- Put the value of a and b in expression,

- Hence

### Answer 8 (B)

- Given problem,
- We know the identities that,

- Compare our equation with identities expression than,

- Hence
- Put the value of a and b in expression,

- Hence,

### Answer 9 (A)

- We know the identities that

- Compare our equation with identities expression than,

- Put the values of a and b in expression than,

### Answer 9 (B)

- We know the identities that

- Compare our equation with identities expression than,

- Put the values of a and b in expression than,

### Answer 10 (A)

- Given algebraic expression,

- We know the identities that ,

- Now compare our polynomial with identities than,

- Now,

### Answer 10 (B)

- Given algebraic expression,

- We know the identities that ,

- Now compare our polynomial with identities than,

- Now,

### Answer 11 (A)

- We know the identities expression that,

- Hence,

- Now put the value of in above equation,

### Answer 11 (B)

- We know the identities expression that,

- Hence,

- Now put the value of in above equation,

- We know the identities expression that,

- Hence

- Now put the value of and In above equation,

### Answer 12 (A)

- We know the identities that,

- Hence

- Now put the value of in above equation than,

- Now we know the identities expression that,

- We put

- Put the value of and

### Answer 13 (A)

- We know the identities that,

- Now put the value of

- Now put the value of in above equation than,

- Now we know the identities expression that,

- we put

- Put the value of