FORMULA FOR a minus b WHOLE SQUARE

In this section, you will learn the formula or expansion  for (a - b)2.

That is, 

(a - b)2  =  (a - b)(a - b)

(a - b)2  =  a2 - ab - ab + b2

(a - b)2  =  a2 - 2ab + b2

Solved Problems

Problem 1 : 

Expand : 

(p - q)

Solution :

(p - q)is in the form of (a - b)2

Comparing (a - b)2 and (p - q)2, we get

a  =  p

b  =  q

Write the formula / expansion for (a - b)2.

(a - b)2  =  a2 - 2ab + b2

Substitute p for a and q for b. 

(p - q)2  =  p2 - 2(p)(q) + q2

(p - q)2  =  p2 - 2pq - q2

So, the expansion of (p - q)2 is

p2 - 2pq + q2

Problem 2 :

Expand : 

(x - 5)

Solution :

(x - 5)is in the form of (a - b)2

Comparing (a - b)and (x - 5)2, we get

a  =  x

b  =  5

Write the formula / expansion for (a - b)2.

(a - b)2  =  a2 - 2ab + b2

Substitute x for a and 5 for b. 

(x - 5)2  =  x2 - 2(x)(5) + 52

(x - 5)2  =  x2 - 10x + 25

So, the expansion of (x - 5)2 is

x2 - 10x + 25

Problem 3 :

Expand : 

(5x - 3)

Solution :

(5x - 3)is in the form of (a - b)2

Comparing (a - b)and (5x - 3)2, we get

a  =  5x

b  =  3

Write the expansion for (a - b)2.

(a - b)2  =  a2 - 2ab + b2

Substitute 5x for a and 3 for b. 

(5x - 3)2  =  (5x)2 - 2(5x)(3) + 32

(5x - 3)2  =  25x2 - 30x + 9

So, the expansion of (5x - 3)2 is

25x2 - 30x + 9

Problem 4 : 

If a - b  =  3 and a2 + b2  =  29, then find the value of ab. 

Solution :

To get the value of ab, we can use the formula or expansion of (a - b)2.

Write the formula / expansion for (a - b)2.

(a - b)2  =  a2 - 2ab + b2

or

(a - b)2  =  a2 + b- 2ab

Substitute 3 for (a - b)  and 29 for (a2 + b2).

32  =  29 - 2ab

9  =  29 - 2ab

Subtract 29 from each side. 

-20  =  -2ab

Divide each side by (-2). 

10  =  ab

So, the value of ab is 10. 

Problem 5 :

Find the value of :

(√2 - 1/√2)2

Solution :

 (√2 - 1/√2)2 is in the form of (a - b)2

Comparing (a - b)and (√2 - 1/√2)2, we get

a  =  √2

b  =  1/√2

Write the formula / expansion for (a - b)2.

(a - b)2  =  a2 - 2ab + b2

Substitute √2 for a and 1/√2 for b. 


(√2
 - 1/√2)2  =  (√2)2 - 2(√2)(1/√2) + (1/√2)2

(√2 - 1/√2)2  =  2 - 2 + 1/2

(√2 - 1/√2)2  =  1/2

So, the value of (√2 - 1/√2)is

1 / 2

Problem 6 :

Find the value of :

(95)2  

Solution :

Instead of multiplying 95 by 95 to get the value of (95)2, we can use the algebraic formula for (a - b)and find the value of (95)easily.

Write (95)in the form of (a - b)2.

(95)2  =  (100 - 5)2

Write the formula / expansion for (a - b)2.

(a - b)2  =  a2 - 2ab + b2

Substitute 100 for a and 5 for b. 


(100
 - 5)2  =  (100)2 - 2(100)(5) + (5)2

(100 - 5)2  =  10000 - 1000 + 25

(95)2  =  9025

So, the value of (95)2 is

9025

Algebraic Identities

Algebraic identities are equalities which remain true regardless of the values of any variables which appear within it.

To know more identities in Algebra, 

Please click here

In our website, we have provided two calculators for algebra identities.

One is to find the expansion for (a + b)n and other one is to find the expansion for (a - b)n.  

Please click the below links to get expansion calculator that you need.  

Expansion Calculator for (a + b)n

Expansion Calculator for (a - b)n

If you would like to have problems on algebraic identities, please click the link given below. 

Worksheet on Algebraic Identities

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Solo Build It!

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. Word Problems Involving Linear Equations

    Aug 14, 22 09:31 PM

    Word Problems Involving Linear Equations

    Read More

  2. Solving System of Linear Equations Word Problems Worksheet

    Aug 14, 22 09:17 PM

    Solving System of Linear Equations Word Problems Worksheet

    Read More

  3. Solving Word Problems with Linear Equations Worksheet

    Aug 14, 22 09:08 PM

    Solving Word Problems with Linear Equations Worksheet

    Read More