Question

Find the following squares by using the identities. ( y - 7 ) ² ( b) (103)²​

Answer 1

${\large{\pmb{\sf{\underline{Required \; Solution...}}}}}$

${\quad \quad \quad{\pmb{\sf{\circ \: \: Question...}}}}$

➼ Find the following squares by using the identities.

• (y-7)²
• (103)²

${\quad \quad \quad{\pmb{\sf{\circ \: \: Solution...}}}}$

➼ Find the following squares by using the identities.

• (y-7)² = y² - 14y + 49
• (103)² = 10609

${\quad \quad \quad{\pmb{\sf{\circ \: \: Using \; identities...}}}}$

${\small{\underline{\boxed{\sf{(a-b)^{2} \: = a^{2} - 2ab + b^{2}}}}}}$

${\small{\underline{\boxed{\sf{(a+b)^{2} \: = a^{2} + 2ab + b^{2}}}}}}$

${\quad \quad \quad{\pmb{\sf{\circ \: \: Full \; Solution...}}}}$

➼ Solution for question's part number (1).

Solution is given below -

${\sf{:\implies (y-7)^{2}}}$

${\small{\underline{\boxed{\sf{(a-b)^{2} \: = a^{2} - 2ab + b^{2}}}}}}$

${\sf{:\implies (a-b)^{2} \: = a^{2} - 2ab + b^{2}}}$

• [Here, a = y and b = 7]

${\sf{:\implies (y-7)^{2} \: = (y)^{2} - 2(y)(7) + (7)^{2}}}$

${\sf{:\implies (y)^{2} - 14y + 49}}$

Let's verify the result too. Verification is given below -

${\sf{:\implies (y-7)^{2}}}$

${\sf{:\implies (y-7)(y-7)}}$

${\sf{:\implies y(y-7) - 7(y-7)}}$

${\sf{:\implies y^{2} - 7y - 7y + 49}}$

${\sf{:\implies y^{2} - 14y + 49}}$

Henceforth, verified !

➼ Solution for question's part number (2).

Solution is given below -

${\sf{:\implies (103)^{2}}}$

${\sf{:\implies (100+3)^{2}}}$

${\small{\underline{\boxed{\sf{(a+b)^{2} \: = a^{2} + 2ab + b^{2}}}}}}$

${\sf{:\implies (a+b)^{2} \: = a^{2} + 2ab + b^{2}}}$

${\sf{:\implies (100)^{2} + 2(100)(3) + (3)^{2}}}$

${\sf{:\implies 10000 + 2(300) + 9}}$

${\sf{:\implies 10000 + 600 + 9}}$

${\sf{:\implies 10600 + 9}}$

${\sf{:\implies 10609}}$