Processing math: 100%

Subscribe to our YouTube channel for the latest videos, updates, and tips.


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 = a2 ± 2ab + b2 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, a2 + b2 = 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, a2 + b2 + c2 = 38.

ab + bc + ca = 12{(a + b + c)2 – (a2 + b2 + c2)} = 12{102 – 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, x2 + y2 = 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: a2 + b2 + c2 = 14, ab + bc + ca = 11.

(a + b + c)2 = a2 + b2 + c2 + 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 = (1.813+(2.19)31.81+2.19

                   = 14{(1.81 + 2.19)3 – 3 × 1.81 × 2.19(1.81 + 2.19)}

                   = 14{43 – 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 454 respectively, find the sum of their cubes.

[Hint: Here, a + b = 7, ab = 454. To find a3 + b3.]

(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 a3 - b3.]


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) 4274

(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. 8 Times Table | Multiplication Table of 8 | Read Eight Times Table

    May 18, 25 04:33 PM

    Printable eight times table
    In 8 times table we will memorize the multiplication table. Printable multiplication table is also available for the homeschoolers. 8 × 0 = 0 8 × 1 = 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40

    Read More

  2. Worksheet on Average | Word Problem on Average | Questions on Average

    May 17, 25 05:37 PM

    In worksheet on average interest we will solve 10 different types of question. Find the average of first 10 prime numbers. The average height of a family of five is 150 cm. If the heights of 4 family

    Read More

  3. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  4. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  5. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More