Question

2. Using the identity (a + b)' = a + b2 + 2ab br (a - b) = a + b2 - 2ab, find the squares of the following 38​

Answer 1

Answer:

1444

Explanation:

(40-2)^2 =(40)^2 +(2)^2 -(2*40*2)

              =(1600+4)-160

              =1604-160

              =1444

Answer 2

Question :-

Using the identities , ( a + b )² = a² + b² + 2ab ( or ) ( a - b )² = a² + b² - 2ab . Find the square of 38

Required to find :-

• Square of 38 ?

Condition mentioned :-

Use the identities ;

• ( a + b )² = a² + b² + 2ab

or

• ( a - b )² = a² + b² - 2ab

Solution :-

We can solve this questions using both identities . This means that we have 2 different solutions for this numerical .

1st solution ( using the 1st identity ) :-

38 can be splited as ;

( 30 + 8 )

Squaring the above one

( 30 + 8 )²

This is in the form of ;

• ( a + b )² = a² + 2ab + b²

So,

( 30 + 8 )² =

( 30 )² + 2 ( 30 ) ( 8 ) + ( 8 )²

900 + 480 + 64

1,444

Hence,

( 30 + 8 )² = 1,444

Similarly,

2nd solution ( using the 2nd identity ) :-

Now,

38 can be splited as ;

( 40 - 2 )

Squaring the above one

( 40 - 2 )²

This is in the form of ;

• ( x - y )² = x² - 2xy + y²

So,

( 40 - 2 )² =

( 40 )² - 2 ( 40 ) ( 2 ) + ( 2 )²

1600 - 160 + 4

1604 - 160

1,444

Hence,

( 40 - 2 )² = 1,444

Therefore

• The square of 38 is 1444

Verification :-

Let's find the square of 1444

$\large{\rm{\bf{ \sqrt{ 1444 } = 38 }}}$

$\big( \tt{ Since \ 38 \times 38 = 1444 } \big)$