**Find the value of the polynomial a3+3a2b+2ab−b2 at a=−2 and b=3. [2 MARKS]**

__Question:__**Options:**

: Steps: 1 Mark

Answer: 1 Mark

The value of the polynomial a3+3a2b+2ab−b2

^{}at a = -2 and b = 3

a3+3a2b+2ab−b2

On substituting the values of a and b in the above expression we get:

=(−2)3+3×(−2)2×3+2×(−2)×3−32

=−8+36−12−9=7

So, thevalue of the polynomial a3+3a2b+2ab−b2 at a=−2 and b=3 is 7.

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## More Questions on This Topic :

**Write the steps which should be followed to check if two terms are like or unlike. Are x2y and xy like terms? [3 MARKS]**

__Question 1.__: Steps: 2 Marks

Answer: 1 Mark

Steps to be followed to decide whether the given terms are like or not are as followed:

i) Ignore the numerical coefficients.

ii) Check the variables in the terms. They must be same otherwise they are unlike terms.

iii) Next, check the powers of each variable in the terms. They should be the same and if they are not then they are not like terms.

We have to check if x2andxy are like terms.

The variables in both these expressions are xandy.

The power of y is equal in both the expressions.

But the power of x in the term x2y is 2, while in the term xy it is one.

∴ The terms are not like.

**Remit's mother gave him Rs. 3xy2 and his father gave him Rs 5(xy2+2).Out of this total money, he spent Rs.(10−3xy2) on his birthday party. How much money is left with him? If x=2 and y=3 find the total amount left with him. [4 MARKS]**

__Question 2.__: Forming the equation: 1 Mark

Steps: 2 Marks

Result: 1 Mark As per the question,

The amount of money given by Remits' motherRs3xy2.

The amount of money given by Remits'fatherRs5(xy2+2).

Total amount =3xy2+5xy2+10=3xy2+5xy2+10=8xy2+10

Total amount Remit spent =10−3xy2

Amount of money left =(8xy2+10)−(10−3xy2)=8xy2+10−10+3xy2=Rs.11xy2

Now if x=2andy=3, then on substituting the values we get,

Amount of money left with

= 11×2××3×3 = Rs198

Hence, the amount of money left with Remit isRs198.

**The number 5 is added to three times the product of two numbers, m, and n. What is the expression formed? What is the value of the expression if m is 4 and n is 5? [2 MARKS]**

__Question 3.__: Forming the expression: 1 Mark

Value of expression: 1 Mark

The product of two numbers, m, and n is

m×n.

Three times the product is 3mn.

Adding 5to three times the product

=5 + 3mn

The expression formed is5 + 3mn

The value of the product at m = 4 and n = 5

=5+3×4×5=65

Hence, thevalue of the expression if m = 4 and n = 5 is 65.

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