## FORMULA FOR a SQUARED MINUS b SQUARE

In this section, we are going to see the formula or factored form of (a2 - b2)

That is,

a2 - b2  =  (a + b)(a - b)

## Solved Problems

Problem 1 :

Factor :

x2 - y2

Solution :

x2 - yis in the form of a2 - b2

Comparing  a2 - b2 and  x2 - y2, we get

a  =  x

b  =  y

Write the formula for  a2 - b2.

a2 - b=  (a + b)(a - b)

Substitute x for a and y for b.

x2 - y2  =  (x + y)(x - y)

So, the factors of x2 - yare

(x + y) and (x - y)

Problem 2 :

Factor :

x2 - 4

Solution :

(x2 - 4) can be written as

x2 - 22

x2 - 22 is in the form of a2 - b2

Comparing  a2 - b2 and  x2 - 22, we get

a  =  x

b  =  2

Write the formula for  a2 - b2.

a2 - b2  =  (a + b)(a - b)

Substitute x for a and 2 for b.

x2 - 22  =  (x + 2)(x - 2)

So, the factors of x2 - 4 are

(x + 2) and (x - 2)

Problem 3 :

Factor :

25x2 - 9

Solution :

(25x2 - 9) can be written as

(5x)2 - 32

(5x)2 - 32 is in the form of a2 - b2

Comparing  a2 - b2 and  (5x)2 - 32, we get

a  =  5x

b  =  3

Write the formula for  a2 - b2.

a2 - b2  =  (a + b)(a - b)

Substitute 5x for a and 3 for b.

(5x)2 - 32  =  (5x + 3)(5x - 3)

So, the factors of 25x2 - 9 are

(5x + 3) and (5x - 3)

Problem 4 :

If x2 - y2  =  16 and x + y  =  8, then find the value of

(x - y)

Solution :

We can factor (x2 - y2) using the formula

(a2 - b2)  =  (a + b)(a - b)

That is

x2 - y2  =  (x + y)(x - y)

Substitute 16 for (x2 - y2) and 8 for (x + y).

16  =  8(x - y)

Divide each side by 8.

2  =  x - y

So, the value of (x - y) is 2.

Problem 5 :

If 36x2 - 9y2  =  52 and 6x - 3y  =  4, then find the value of

(6x + 3y)

Solution :

We can factor (36x2 - 9y2) using the formula

(a2 - b2)  =  (a + b)(a - b)

That is

36x2 - 9y2  =  (6x)2 - (3y)2

36x2 - 9y2  =  (6x + 3y)(6x - 3y)

Substitute 52 for (36x2 - 9y2) and 4 for (6x - 3y).

52  =  (6x + 3y) ⋅ 4

Divide each side by 4.

13  =  6x + 3y

So, the value of (6x + 3y) is 13.

Problem 6 :

Find the value of the numerical expression given below using algebraic identity.

(12)2 / 96

Solution :

(12)2 / 96  =  (12)2 / (100 - 4)

(12)2 / 96  =  (12)2 / (102 - 22)

Factor (102 - 22) using the formula for (a2 - b2).

(12)2 / 96  =  (12)2 / [(10 + 2)(10 - 2)]

(12)2 / 96  =  (12)2 / [(12)(8)]

(12)2 / 96  =  12 / 8

(12)2 / 96  =  3 / 2

So, the value of (12)2 / 96 is

3/2

## 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,

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

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.

If you have any feedback about our math content, please mail us :

v4formath@gmail.com

You can also visit the following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6