Question

(A-B)²=A²-2AB+B²
verify it​

Answer 1

Answer:

Step-by-step explanation:

This called the perfect square formula

A = 6

B = 5

(6 - 5)^2 = 1

6^2 - 2 x 6 x 5 + 5^2 = 1

This formula works for all integers

Answer 2

Topic

Algebraic Identities

To Verify

( a - b )² = a² - 2ab + b²

Solution

Technique 1

To verify the identity,

• Take different values of a and b
• Check whether these values satisfy the identity or not.

Now,

Taking a = 5 and b = 1

Solving LHS,

( 5 - 1 )²

4²

16

Solving RHS,

5² - 2( 5 )( 1 ) + 1²

25 - 10 + 1

26 - 10

16

Given identity is true for these values.

Now,

Take a = 8 and b = 2

Solving LHS,

( 8 - 2 )²

6²

36

Solving RHS,

8² - 2(8)(2) + 2²

64 - 32 + 4

68 - 32

36

Given identity is true for these values also.

So, we can say that this identity is true for all different values of a and b.

Hence, verified.

Technique 2

We can use simple algebraic multiplication.

( a - b )² = ( a - b ) × ( a - b )

Now, we will do multiplication

( a - b ) × ( a - b )

a( a - b ) - b( a - b )

a² - ab - ba + b²

a² - 2ab + b²

( Note: ab = ba )

So, we can write

( a - b )² = a² - 2ab + b²

Hence, verified.