Question

नंबर ऑफ फैक्टर ऑफ ए प्लस बी स्क्वायर इज​

Answer 1

Answer:

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 - y2 is 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 - b2 = (a + b)(a - b)

Substitute x for a and y for b.

x2 - y2 = (x + y)(x - y)

So, the factors of x2 - y2 are

(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,