Worksheet on Application Problems on Expansion of Powers of Binomials


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.]

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 

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.








Source link

Notice: compact(): Undefined variable: limits in /customers/6/d/3/sciencetells.co.uk/httpd.www/wp-includes/class-wp-comment-query.php on line 853 Notice: compact(): Undefined variable: groupby in /customers/6/d/3/sciencetells.co.uk/httpd.www/wp-includes/class-wp-comment-query.php on line 853