Worksheet on Application Problems on Expansion of Powers of Binomials & Trinomials

Practice the questions given in the worksheet on application problems on expansion of powers of binomials and trinomials.

1. Use (a ± b)\(^{2}\) = a\(^{2}\) ± 2ab + b\(^{2}\) to evaluate the following:

(i) (3.001)\(^{2}\)

(ii) (5.99)\(^{2}\)

(iii) 1001 × 999

(iv) 5.63 × 5.63 + 11.26 × 2.37 + 2.37 × 2.37

(v) 8.79 × 8.79 – 8.79  × 3.58 + 1.79 × 1.79


2. (i) If the sum of two numbers is 12 and the sum of their squares is 74, find the product of the numbers.

[Hint: a + b = 12, a\(^{2}\) + b\(^{2}\) = 74. To find ab.]


(ii) If the numbers x is 5 more than the number y and the sum of the squares of x and y is 37 then find the product of x and y.

(iii) The sum of two numbers is 14 and their difference is 2. Find the product of the two numbers.

[Hint: a + b = 14, a – b = 2. To find ab.]

 

3. (i) If the sum of three numbers is 10 and the sum of their squares is 38, find the sum of the products of the three numbers taking two at a time.

[Hint: a + b + c = 10, a\(^{2}\) + b\(^{2}\) + c\(^{2}\) = 38.

ab + bc + ca = \(\frac{1}{2}\){(a + b + c)\(^{2}\) – (a\(^{2}\) + b\(^{2}\) + c\(^{2}\))} = \(\frac{1}{2}\){10\(^{2}\) – 38}.]


(ii) If the sum of the squares of the squares of three numbers is equal to the square of their sum, prove that the sum of the products of the three numbers taking two at a time is equal to zero.  

[Hint: x - y = 5, x\(^{2}\) + y\(^{2}\) = 37. To find xy.]


(iii)If the sum of the squares of three positive numbers is 14 and the sum of their products taking two at a time is 11, find the sum of the numbers.

[Hint: a\(^{2}\) + b\(^{2}\) + c\(^{2}\) = 14, ab + bc + ca = 11.

(a + b + c)\(^{2}\) = a\(^{2}\) + b\(^{2}\) + c\(^{2}\) + 2(ab + bc + ca) = 14 + 2 × 11 = 36.]


4. Find the value:

(i) (5.45)\(^{3}\) + (3.55)\(^{3}\)

(ii) (8.12)\(^{3}\) – (3.12)\(^{3}\)

(iii) 1.81 × 1.81 – 1.81 × 2.19 + 2.19 × 2.19

[Hint: Value = \(\frac{(1.81^{3} + (2.19)^{3}}{1.81 + 2.19}\)

                   = \(\frac{1}{4}\){(1.81 + 2.19)\(^{3}\) – 3 × 1.81 × 2.19(1.81 + 2.19)}

                   = \(\frac{1}{4}\){4\(^{3}\) – 12 × 1.81 × 2.19}]

 

(iv) 7.16 × 7.16 + 2.16 × 7.16 + 2.16 × 2.16


5. (i) If the sum of and product of two numbers are 7 and \(\frac{45}{4}\) respectively, find the sum of their cubes.

[Hint: Here, a + b = 7, ab = \(\frac{45}{4}\). To find a\(^{3}\) + b\(^{3}\).]

(ii) If the difference of two numbers is 10 and their product is – 24, find the difference of their cubes.

[Hint: Here, a - b = 10, ab = -24. To find a\(^{3}\) - b\(^{3}\).]


Answers for the worksheet on application problems on expansion of powers of binomials and trinomials are given below.


Answer:


1. (i) 9.006001

(ii) 35.8801

(iii) 999999

(iv) 64

(v) 49


2. (i) 35 

(ii) 6 

(iii) 48 

 

3. (i) 31 

(iii) 6 


4. (i) 206.6175

(ii) 505.016

(iii) 4.1083

(iv) 71.3968


5. (i) \(\frac{427}{4}\)

(ii) 280




9th Grade Math

From Worksheet on Application Problems on Expansion of Powers of Binomials and Trinomials to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Decimal Place Value Chart |Tenths Place |Hundredths Place |Thousandths

    Jul 19, 24 03:26 PM

    Decimal place value chart
    Decimal place value chart are discussed here: The first place after the decimal is got by dividing the number by 10; it is called the tenths place.

    Read More

  2. Definition of Decimal Numbers | Decimal Part | Decimal Point |Examples

    Jul 19, 24 11:13 AM

    Decimal Numbers
    Definition of decimal numbers: We have learnt that the decimals are an extension of our number system. We also know that decimals can be considered as fractions whose denominators are 10, 100, 1000

    Read More

  3. Addition and Subtraction of Fractions | Solved Examples | Worksheet

    Jul 19, 24 02:00 AM

    Addition and subtraction of fractions are discussed here with examples. To add or subtract two or more fractions, proceed as under: (i) Convert the mixed fractions (if any.) or natural numbers

    Read More

  4. Fractions in Descending Order |Arranging Fractions an Descending Order

    Jul 19, 24 02:00 AM

    We will discuss here how to arrange the fractions in descending order. Solved examples for arranging in descending order: 1. Arrange the following fractions 5/6, 7/10, 11/20 in descending order. First…

    Read More

  5. Fractions in Ascending Order | Arranging Fractions | Worksheet |Answer

    Jul 19, 24 01:59 AM

    Comparison Fractions
    We will discuss here how to arrange the fractions in ascending order. Solved examples for arranging in ascending order: 1. Arrange the following fractions 5/6, 8/9, 2/3 in ascending order. First we fi…

    Read More