Question

verily each of the following Identities for a=1 and b=2.
(al (a+b)²=a+2ab+b²
(b) (a-b)² a²-2ab+b²
(c) (a+b) (a-b) = a²-b²​

Answer 1

Question:-

Verify each of the following identities a = 1 and b = 2

a. (a + b)² = a + 2ab + b²

b. (a - b)² = a² - 2ab + b²

c. (a + b) (a - b) = a² - b²

Solution:-

a.

(a + b)² = a + 2ab + b²

(1 + 2)² = 1² + 2( 1 )( 2 ) + 2²

3² = 1 + 4 + 4

$\boxed{\bf{\color{yelow}{ \: 9 \: = \: 9 \: }}}$

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b.

(a - b)² = a² - 2ab + b²

(1 - 2)² = 1² - 2( 1 )( 2 ) + 2²

-1² = 1 - 4 + 4

$\boxed{\bf{\color{yelow}{ \: 1 \: = \: 1 \: }}}$

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c.

(a + b) (a - b) = a² - b²

(1 + 2) (1 - 2) = 1² - 2²

( 3 ) ( -1 ) = 1 - 4

$\boxed{\bf{\color{yelow}{ \: -3 \: = \: -3 \: }}}$

$\boxed{\bf{\color{yelow}{ \: Hence Verified \: }}}$

Answer 2

__________________________

a.

(a + b)² = a + 2ab + b²

(1 + 2)² = 1² + 2( 1 )( 2 ) + 2²

3² = 1 + 4 + 4

9=9

___________________________

b.

(a-b)² a²-2ab+b²

(1 - 2)² = 1² - 2( 1 )( 2 ) + 2²

-1² = 1 - 4 + 4

1=1

___________________________

c.

(a + b) (a - b) = a² - b²

(1 + 2) (1 - 2) = 1² - 2²

( 3 ) ( -1 ) = 1 - 4

-3=-3

____________________________

$\huge{\boxed{\bf{hence\: verified!}}}$