Question

find the following product using appor
identies?(y-1) (y-1) ​

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

In question given (y-1)(y-1)

It means (y-1) is occuring two times Here ,we can also write (y-1)(y-1) as $\bold{{(y - 1)}^{2} }$

Here ,this identity is used:-

$\bold{\boxed{\purple{{(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy}}}$

${(y - 1)}^{2} = {y}^{2} + {(1)}^{2} - 2(y)(1)$

${(y - 1)}^{2} = {y}^{2} + 1 - 2y$

ㅤㅤㅤㅤㅤㅤㅤOr

$\bold{\bold{ = > {y}^{2} + 2y - 1}}$

ㅤㅤㅤㅤㅤ

Other related identity:-

$\bold{\boxed{ {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy}}$

$\bold{\boxed{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3 {x}^{2} y + 3x {y}^{2}}}$

$\bold{\boxed{{x}^{2} + {y}^{2} = (x + y)(x - y)}}$

$\bold{\boxed{{x}^{3} + {y}^{3} = (x + y)[{x}^{2} - xy + {y}^{2} ]}}$

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

In question given (y-1)(y-1)

It means (y-1) is occuring two times Here ,we can also write (y-1)(y-1) as $\bold{{(y - 1)}^{2} }$

Here ,this identity is used:-

$\bold{\boxed{\purple{{(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy}}}$

${(y - 1)}^{2} = {y}^{2} + {(1)}^{2} - 2(y)(1)$

${(y - 1)}^{2} = {y}^{2} + 1 - 2y$

ㅤㅤㅤㅤㅤㅤㅤOr

$\bold{\bold{ = > {y}^{2} + 2y - 1}}$

ㅤㅤㅤㅤㅤ

Other related identity:-

$\bold{\boxed{ {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy}}$

$\bold{\boxed{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3 {x}^{2} y + 3x {y}^{2}}}$

$\bold{\boxed{{x}^{2} + {y}^{2} = (x + y)(x - y)}}$

$\bold{\boxed{{x}^{3} + {y}^{3} = (x + y)[{x}^{2} - xy + {y}^{2} ]}}$