Find the value by using suitable identity.
(a) $(2y+1)^2$(b) $95\times105$

Given:
 (a) $(2y+1)^2$

(b) $95\times105$

To do:

We have to find the values by using suitable identities.

Solution:

We know that,

$(a+b)^2=a^2+2ab+b^2$

$(a+b)(c-d)=a\times c-a\times d+b\times c-b\times d$

Therefore,

(a) $(2y+1)^2=(2y)^2+2(2y)(1)+(1)^2$    (Using $(a+b)^2=a^2+2ab+b^2$)

$=4y^2+4y+1$.

(b) $95\times105$ can be written as $(100-5)\times(100+5)$

$95\times105=(100-5)\times(100+5)$

$=100\times 100+100\times 5-5\times 100-5\times 5$ (Using $(a+b)(c-d)=a\times c-a\times d+b\times c-b\times d$)

$=10000+500-500-25$

$=9975$.

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Updated on: 10-Oct-2022

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