Which of the following is an identity?

1

(a)

(b+c)=b²+c²

(b)

b²-c²=(b+c)²-4bc

(c)

b²-c² =(b-c)²

(d)

(b+ c)² =b² + 2bc+c²

Which of the following is a binomial?

1

(a)

13xb+b

(b)

6b²+7a+2c

(c)

45(b²+ a)

(d)

13ax3bx5c

Sum of a - b + ab, b + c - bc and c - a - ac is

1

(a)

ab-2c+ac-bc

(b)

2c-ab-ac-bc

(c)

2c+ab-ac-bc

(d)

2c-ab+ac-bc

Area of a rectangle with length 5ab and breadth 13ac² is

1

(a)

65a²bc

(b)

35a²bc²

(c)

65a²bc²

(d)

65abc²

Product of the monomials, -15p, -13q², pq is

1

(a)

-165p²q³

(b)

195p²q³

(c)

195p³q²

(d)

-195p³q²

Square of (3a+5b) is________

1

(a)

∵(3a+5)²=(3a)²+2.(3a).(5b)+(5b)²=9a²+30ab+25b²

The product of two terms with like signs is a__________term

1

(a)

(-a)\(\times \)(-a)²=a3 and (ab)\(\times \)(b²)=ab³​​​​​​​

The product of two terms with unlike signs is a______________term

1

(a)

(-a)\(\times \)a²=-a3 and (-ab)\(\times \)(b²)=-ab³​​​​​​​​​​​​​​

The sum of 13pq² and -7q²p is_______

1

(a)

\(\because\) 13pq²-7q²p=6pq²

On subtracting -3a²b² from a²b², we get_______

1

(a)

\(\because\) a²b²-(-3a²b²)=a²b²+3a²b²=4a²b²

The value of (a + b)² + (a - b)² is 4ab.

1

(a) True

(b) False

The difference of the squares of two consecutive numbers is their sum

1

(a) False

(b) True

Sum of 16a²bc, - 8b²ac and 8a²bc is 16a²bc.

1

(a) True

(b) False

Like term as 15a³b² is 25a³b²c.

1

(a) True

(b) False

The product of 24xyz² and 3xy² is 72x²y³z². Match the Columns

1

(a) False

(b) True

Identify the terms, their coefficients for each of the following expressions,
3- pq+ qr- rp

2

(a)

Add the following 2p²q² - 3pq + 4,5 + 7pq - 3p²q²

2

(a)

Find the product of the following pairs of monomials - 4p,7p

2

(a)

Obtain the product of m, - mn,mnp

2

(a)

Express the following product as a monomial \(\left( { a }^{ 4 } \right) \times \left( { 2a }^{ 3 } \right) \times \left( \frac { 1 }{ 5 } { a }^{ 2 } \right) \times \left( -5a \right) \)

2

(a)

Write two like terms of the following
7xy

3

(a)

Show that a² + 3a+ 2= 132 is not true for a=-5 and for a= 0.

3

(a)

Simplify (3x + 2y)² + (3x- 2y)².

3

(a)

Solve the following using identities.47\(\times\)53

3

(a)

Solve the following using identities.104\(\times\)97

3

(a)

If 2x + 3y =5 and xy =1, then find the value of 4x² + 9y².

5

(a)

One day, Sahil went to playa cricket tournament (organised in a sports complex) along with his two friends Rahul and Sunil. Someone stole Sahil's bicycle but Rahul and Sunil helped him to buy a new one bicycle contributing rs(2x +80) and rs (8x + 20), respectively, If the bicycle costs rs. 2100,
(a) what were the amount given by Rahul and Sunil to Sahil?
(b) what are the values depicted by Rahul and Sunil here?

5

(a)