Question

evaluate 109×91.using the suitable identity.

Answer 1

= 109 × 91

= (100+9)(100-9)

BY USING IDENTITY, a^2 - b^2 = (a+b)(a-b)

= (100)^2 - (9)^2

= 10000-81

= 9919

HOPE THIS WILL HELP YOU

Answer 2

Answer:

The evaluated value of 109×91 is 9919.

Step-by-step explanation:

The identity used here is : $(a+b)\times(a-b)= (a^{2} -b^{2} )$

109×91 = (100+9)×(100-9)

∴

109×91 = (100² - 9²)

=(10000-81)

=9919

The correct answer is 9919.

Some important algebraic identities are as follows:

1. $(a+b)^{2} = (a^{2}+2a\times b+b^{2} )$
2. $(a-b)^{2} = (a^{2} -2a\times b +b^{2})$
3. $(a+b)\times(a-b) = (a^{2} -b^{2})$
4. $(a+b)^{2}+(a-b)^{2} =2(a^{2} +b^{2} )$
5. $(a+b)^{2} -(a-b)^{2} =4a\times b$